The Alternating Knot 10₁₁₈

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Acknowledgement

KnotPlot

PD Presentation: X₆₂₇₁ X_18,6,19,5 X_20,13,1,14 X_12,19,13,20 X_14,7,15,8 X₈₃₉₄ X_2,16,3,15 X_10,18,11,17 X_16,10,17,9 X_4,11,5,12

Gauss Code: {1, -7, 6, -10, 2, -1, 5, -6, 9, -8, 10, -4, 3, -5, 7, -9, 8, -2, 4, -3}

DT (Dowker-Thistlethwaite) Code: 6 8 18 14 16 4 20 2 10 12

Minimum Braid Representative:

Length is 10, width is 3
Braid index is 3

A Morse Link Presentation:

3D Invariants:

Symmetry Type Unknotting Number 3-Genus Bridge/Super Bridge Index Nakanishi Index

NegativeAmphicheiral 1 4 3 / NotAvailable 1

Alexander Polynomial: t^-4 - 5t^-3 + 12t^-2 - 19t^-1 + 23 - 19t + 12t² - 5t³ + t⁴

Conway Polynomial: 1 + 2z⁴ + 3z⁶ + z⁸

Other knots with the same Alexander/Conway Polynomial: {K11a257, ...}

Determinant and Signature: {97, 0}

Jones Polynomial: - q^-5 + 4q^-4 - 8q^-3 + 12q^-2 - 15q^-1 + 17 - 15q + 12q² - 8q³ + 4q⁴ - q⁵

Other knots (up to mirrors) with the same Jones Polynomial: {...}

A2 (sl(3)) Invariant: - q^-14 + 2q^-12 - 2q^-10 + 2q^-8 - 2q^-4 + 4q^-2 - 3 + 4q² - 2q⁴ + 2q⁸ - 2q¹⁰ + 2q¹² - q¹⁴

HOMFLY-PT Polynomial: - 2a^-2z² - 3a^-2z⁴ - a^-2z⁶ + 1 + 4z² + 8z⁴ + 5z⁶ + z⁸ - 2a²z² - 3a²z⁴ - a²z⁶

Kauffman Polynomial: - a^-5z³ + a^-5z⁵ + a^-4z² - 6a^-4z⁴ + 4a^-4z⁶ - a^-3z + 5a^-3z³ - 12a^-3z⁵ + 7a^-3z⁷ - 2a^-2z² + 6a^-2z⁴ - 11a^-2z⁶ + 7a^-2z⁸ - 3a^-1z + 15a^-1z³ - 20a^-1z⁵ + 6a^-1z⁷ + 3a^-1z⁹ + 1 - 6z² + 24z⁴ - 30z⁶ + 14z⁸ - 3az + 15az³ - 20az⁵ + 6az⁷ + 3az⁹ - 2a²z² + 6a²z⁴ - 11a²z⁶ + 7a²z⁸ - a³z + 5a³z³ - 12a³z⁵ + 7a³z⁷ + a⁴z² - 6a⁴z⁴ + 4a⁴z⁶ - a⁵z³ + a⁵z⁵

V₂ and V₃, the type 2 and 3 Vassiliev invariants: {0, 0}

Khovanov Homology:
(The squares with yellow highlighting are those on the "critical diagonals", where j-2r=s+1 or j-2r=s+1, where s=0 is the signature of 10₁₁₈. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.)

t^rq^j r = -5 r = -4 r = -3 r = -2 r = -1 r = 0 r = 1 r = 2 r = 3 r = 4 r = 5

j = 11 1

j = 9 3

j = 7 5 1

j = 5 7 3

j = 3 8 5

j = 1 9 7

j = -1 7 9

j = -3 5 8

j = -5 3 7

j = -7 1 5

j = -9 3

j = -11 1

n Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2 q^-15 - 4q^-14 + 3q^-13 + 11q^-12 - 27q^-11 + 8q^-10 + 52q^-9 - 76q^-8 - 8q^-7 + 130q^-6 - 122q^-5 - 55q^-4 + 208q^-3 - 134q^-2 - 107q^-1 + 241 - 107q - 134q² + 208q³ - 55q⁴ - 122q⁵ + 130q⁶ - 8q⁷ - 76q⁸ + 52q⁹ + 8q¹⁰ - 27q¹¹ + 11q¹² + 3q¹³ - 4q¹⁴ + q¹⁵

3 - q^-30 + 4q^-29 - 3q^-28 - 6q^-27 + 4q^-26 + 18q^-25 - 9q^-24 - 48q^-23 + 21q^-22 + 99q^-21 - 14q^-20 - 194q^-19 - 26q^-18 + 323q^-17 + 129q^-16 - 466q^-15 - 307q^-14 + 582q^-13 + 562q^-12 - 650q^-11 - 851q^-10 + 639q^-9 + 1148q^-8 - 565q^-7 - 1402q^-6 + 430q^-5 + 1603q^-4 - 274q^-3 - 1714q^-2 + 84q^-1 + 1769 + 84q - 1714q² - 274q³ + 1603q⁴ + 430q⁵ - 1402q⁶ - 565q⁷ + 1148q⁸ + 639q⁹ - 851q¹⁰ - 650q¹¹ + 562q¹² + 582q¹³ - 307q¹⁴ - 466q¹⁵ + 129q¹⁶ + 323q¹⁷ - 26q¹⁸ - 194q¹⁹ - 14q²⁰ + 99q²¹ + 21q²² - 48q²³ - 9q²⁴ + 18q²⁵ + 4q²⁶ - 6q²⁷ - 3q²⁸ + 4q²⁹ - q³⁰

4 q^-50 - 4q^-49 + 3q^-48 + 6q^-47 - 9q^-46 + 5q^-45 - 17q^-44 + 22q^-43 + 31q^-42 - 60q^-41 - 4q^-40 - 61q^-39 + 131q^-38 + 193q^-37 - 192q^-36 - 199q^-35 - 372q^-34 + 386q^-33 + 907q^-32 - 7q^-31 - 645q^-30 - 1686q^-29 + 78q^-28 + 2318q^-27 + 1584q^-26 - 286q^-25 - 4171q^-24 - 2229q^-23 + 2995q^-22 + 4722q^-21 + 2593q^-20 - 6078q^-19 - 6548q^-18 + 1037q^-17 + 7450q^-16 + 7776q^-15 - 5461q^-14 - 10670q^-13 - 3245q^-12 + 7881q^-11 + 12898q^-10 - 2626q^-9 - 12675q^-8 - 7693q^-7 + 6233q^-6 + 16074q^-5 + 739q^-4 - 12520q^-3 - 10838q^-2 + 3699q^-1 + 17069 + 3699q - 10838q² - 12520q³ + 739q⁴ + 16074q⁵ + 6233q⁶ - 7693q⁷ - 12675q⁸ - 2626q⁹ + 12898q¹⁰ + 7881q¹¹ - 3245q¹² - 10670q¹³ - 5461q¹⁴ + 7776q¹⁵ + 7450q¹⁶ + 1037q¹⁷ - 6548q¹⁸ - 6078q¹⁹ + 2593q²⁰ + 4722q²¹ + 2995q²² - 2229q²³ - 4171q²⁴ - 286q²⁵ + 1584q²⁶ + 2318q²⁷ + 78q²⁸ - 1686q²⁹ - 645q³⁰ - 7q³¹ + 907q³² + 386q³³ - 372q³⁴ - 199q³⁵ - 192q³⁶ + 193q³⁷ + 131q³⁸ - 61q³⁹ - 4q⁴⁰ - 60q⁴¹ + 31q⁴² + 22q⁴³ - 17q⁴⁴ + 5q⁴⁵ - 9q⁴⁶ + 6q⁴⁷ + 3q⁴⁸ - 4q⁴⁹ + q⁵⁰

5 - q^-75 + 4q^-74 - 3q^-73 - 6q^-72 + 9q^-71 - 6q^-69 + 4q^-68 - 5q^-67 - 9q^-66 + 37q^-65 + 29q^-64 - 48q^-63 - 83q^-62 - 68q^-61 + 46q^-60 + 244q^-59 + 301q^-58 - 24q^-57 - 573q^-56 - 787q^-55 - 287q^-54 + 875q^-53 + 1843q^-52 + 1364q^-51 - 921q^-50 - 3428q^-49 - 3602q^-48 - 259q^-47 + 4964q^-46 + 7568q^-45 + 3700q^-44 - 5394q^-43 - 12667q^-42 - 10365q^-41 + 2685q^-40 + 17588q^-39 + 20463q^-38 + 4813q^-37 - 19877q^-36 - 32656q^-35 - 18124q^-34 + 16897q^-33 + 44345q^-32 + 36630q^-31 - 6744q^-30 - 52443q^-29 - 57942q^-28 - 10715q^-27 + 54076q^-26 + 78732q^-25 + 34017q^-24 - 48179q^-23 - 95785q^-22 - 59901q^-21 + 35233q^-20 + 106740q^-19 + 85226q^-18 - 17417q^-17 - 111131q^-16 - 107011q^-15 - 2543q^-14 + 109646q^-13 + 123904q^-12 + 22010q^-11 - 104034q^-10 - 135442q^-9 - 39509q^-8 + 96005q^-7 + 142679q^-6 + 54100q^-5 - 86907q^-4 - 146180q^-3 - 66504q^-2 + 77050q^-1 + 147507 + 77050q - 66504q² - 146180q³ - 86907q⁴ + 54100q⁵ + 142679q⁶ + 96005q⁷ - 39509q⁸ - 135442q⁹ - 104034q¹⁰ + 22010q¹¹ + 123904q¹² + 109646q¹³ - 2543q¹⁴ - 107011q¹⁵ - 111131q¹⁶ - 17417q¹⁷ + 85226q¹⁸ + 106740q¹⁹ + 35233q²⁰ - 59901q²¹ - 95785q²² - 48179q²³ + 34017q²⁴ + 78732q²⁵ + 54076q²⁶ - 10715q²⁷ - 57942q²⁸ - 52443q²⁹ - 6744q³⁰ + 36630q³¹ + 44345q³² + 16897q³³ - 18124q³⁴ - 32656q³⁵ - 19877q³⁶ + 4813q³⁷ + 20463q³⁸ + 17588q³⁹ + 2685q⁴⁰ - 10365q⁴¹ - 12667q⁴² - 5394q⁴³ + 3700q⁴⁴ + 7568q⁴⁵ + 4964q⁴⁶ - 259q⁴⁷ - 3602q⁴⁸ - 3428q⁴⁹ - 921q⁵⁰ + 1364q⁵¹ + 1843q⁵² + 875q⁵³ - 287q⁵⁴ - 787q⁵⁵ - 573q⁵⁶ - 24q⁵⁷ + 301q⁵⁸ + 244q⁵⁹ + 46q⁶⁰ - 68q⁶¹ - 83q⁶² - 48q⁶³ + 29q⁶⁴ + 37q⁶⁵ - 9q⁶⁶ - 5q⁶⁷ + 4q⁶⁸ - 6q⁶⁹ + 9q⁷¹ - 6q⁷² - 3q⁷³ + 4q⁷⁴ - q⁷⁵

6 q^-105 - 4q^-104 + 3q^-103 + 6q^-102 - 9q^-101 + q^-99 + 19q^-98 - 21q^-97 - 17q^-96 + 32q^-95 - 45q^-94 + 8q^-93 + 50q^-92 + 128q^-91 - 41q^-90 - 167q^-89 - 62q^-88 - 286q^-87 - 16q^-86 + 387q^-85 + 900q^-84 + 404q^-83 - 424q^-82 - 881q^-81 - 2094q^-80 - 1401q^-79 + 650q^-78 + 3938q^-77 + 4458q^-76 + 2396q^-75 - 1204q^-74 - 8305q^-73 - 10766q^-72 - 6703q^-71 + 5801q^-70 + 16461q^-69 + 20757q^-68 + 14405q^-67 - 9709q^-66 - 33262q^-65 - 42976q^-64 - 22056q^-63 + 15948q^-62 + 58065q^-61 + 77950q^-60 + 42156q^-59 - 29551q^-58 - 104768q^-57 - 122544q^-56 - 71254q^-55 + 47281q^-54 + 171007q^-53 + 198422q^-52 + 103304q^-51 - 89064q^-50 - 253004q^-49 - 297475q^-48 - 141664q^-47 + 149780q^-46 + 383153q^-45 + 408243q^-44 + 154486q^-43 - 230153q^-42 - 546632q^-41 - 530354q^-40 - 143910q^-39 + 380359q^-38 + 726609q^-37 + 615539q^-36 + 96521q^-35 - 581428q^-34 - 920446q^-33 - 660120q^-32 + 60354q^-31 + 813628q^-30 + 1064305q^-29 + 635918q^-28 - 301929q^-27 - 1072972q^-26 - 1148980q^-25 - 451384q^-24 + 602132q^-23 + 1278685q^-22 + 1132696q^-21 + 144123q^-20 - 950647q^-19 - 1413224q^-18 - 910924q^-17 + 247709q^-16 + 1245688q^-15 + 1420940q^-14 + 538462q^-13 - 703247q^-12 - 1458570q^-11 - 1189250q^-10 - 66498q^-9 + 1100658q^-8 + 1522082q^-7 + 790633q^-6 - 474803q^-5 - 1403113q^-4 - 1322934q^-3 - 286649q^-2 + 950870q^-1 + 1538859 + 950870q - 286649q² - 1322934q³ - 1403113q⁴ - 474803q⁵ + 790633q⁶ + 1522082q⁷ + 1100658q⁸ - 66498q⁹ - 1189250q¹⁰ - 1458570q¹¹ - 703247q¹² + 538462q¹³ + 1420940q¹⁴ + 1245688q¹⁵ + 247709q¹⁶ - 910924q¹⁷ - 1413224q¹⁸ - 950647q¹⁹ + 144123q²⁰ + 1132696q²¹ + 1278685q²² + 602132q²³ - 451384q²⁴ - 1148980q²⁵ - 1072972q²⁶ - 301929q²⁷ + 635918q²⁸ + 1064305q²⁹ + 813628q³⁰ + 60354q³¹ - 660120q³² - 920446q³³ - 581428q³⁴ + 96521q³⁵ + 615539q³⁶ + 726609q³⁷ + 380359q³⁸ - 143910q³⁹ - 530354q⁴⁰ - 546632q⁴¹ - 230153q⁴² + 154486q⁴³ + 408243q⁴⁴ + 383153q⁴⁵ + 149780q⁴⁶ - 141664q⁴⁷ - 297475q⁴⁸ - 253004q⁴⁹ - 89064q⁵⁰ + 103304q⁵¹ + 198422q⁵² + 171007q⁵³ + 47281q⁵⁴ - 71254q⁵⁵ - 122544q⁵⁶ - 104768q⁵⁷ - 29551q⁵⁸ + 42156q⁵⁹ + 77950q⁶⁰ + 58065q⁶¹ + 15948q⁶² - 22056q⁶³ - 42976q⁶⁴ - 33262q⁶⁵ - 9709q⁶⁶ + 14405q⁶⁷ + 20757q⁶⁸ + 16461q⁶⁹ + 5801q⁷⁰ - 6703q⁷¹ - 10766q⁷² - 8305q⁷³ - 1204q⁷⁴ + 2396q⁷⁵ + 4458q⁷⁶ + 3938q⁷⁷ + 650q⁷⁸ - 1401q⁷⁹ - 2094q⁸⁰ - 881q⁸¹ - 424q⁸² + 404q⁸³ + 900q⁸⁴ + 387q⁸⁵ - 16q⁸⁶ - 286q⁸⁷ - 62q⁸⁸ - 167q⁸⁹ - 41q⁹⁰ + 128q⁹¹ + 50q⁹² + 8q⁹³ - 45q⁹⁴ + 32q⁹⁵ - 17q⁹⁶ - 21q⁹⁷ + 19q⁹⁸ + q⁹⁹ - 9q¹⁰¹ + 6q¹⁰² + 3q¹⁰³ - 4q¹⁰⁴ + q¹⁰⁵

7 - q^-140 + 4q^-139 - 3q^-138 - 6q^-137 + 9q^-136 - q^-134 - 14q^-133 - 2q^-132 + 43q^-131 - 6q^-130 - 24q^-129 + 8q^-128 - 27q^-127 - 23q^-126 - 69q^-125 - 8q^-124 + 242q^-123 + 163q^-122 + 35q^-121 - 72q^-120 - 385q^-119 - 411q^-118 - 518q^-117 - 142q^-116 + 1078q^-115 + 1554q^-114 + 1474q^-113 + 483q^-112 - 1739q^-111 - 3318q^-110 - 4454q^-109 - 3310q^-108 + 1813q^-107 + 7114q^-106 + 11157q^-105 + 10245q^-104 + 1633q^-103 - 9940q^-102 - 22433q^-101 - 27507q^-100 - 16520q^-99 + 6677q^-98 + 37057q^-97 + 58407q^-96 + 52468q^-95 + 18370q^-94 - 40973q^-93 - 100446q^-92 - 122513q^-91 - 89098q^-90 + 7781q^-89 + 133531q^-88 + 223614q^-87 + 228198q^-86 + 109054q^-85 - 106363q^-84 - 325147q^-83 - 443178q^-82 - 356501q^-81 - 55497q^-80 + 349552q^-79 + 689017q^-78 + 753321q^-77 + 439152q^-76 - 173905q^-75 - 857942q^-74 - 1254288q^-73 - 1089251q^-72 - 333822q^-71 + 773753q^-70 + 1714946q^-69 + 1964892q^-68 + 1265562q^-67 - 240851q^-66 - 1909001q^-65 - 2902350q^-64 - 2597945q^-63 - 884016q^-62 + 1573715q^-61 + 3625400q^-60 + 4160778q^-59 + 2617311q^-58 - 502842q^-57 - 3814742q^-56 - 5650023q^-55 - 4799031q^-54 - 1364682q^-53 + 3202185q^-52 + 6697142q^-51 + 7115131q^-50 + 3902842q^-49 - 1670439q^-48 - 6984275q^-47 - 9173314q^-46 - 6807311q^-45 - 696117q^-44 + 6335550q^-43 + 10610793q^-42 + 9681809q^-41 + 3632710q^-40 - 4775784q^-39 - 11201786q^-38 - 12142587q^-37 - 6760636q^-36 + 2515244q^-35 + 10900762q^-34 + 13915945q^-33 + 9700418q^-32 + 121154q^-31 - 9843831q^-30 - 14895676q^-29 - 12155512q^-28 - 2782605q^-27 + 8283604q^-26 + 15135646q^-25 + 13970837q^-24 + 5181766q^-23 - 6511733q^-22 - 14808343q^-21 - 15135897q^-20 - 7142924q^-19 + 4783786q^-18 + 14138213q^-17 + 15752305q^-16 + 8612048q^-15 - 3272853q^-14 - 13335658q^-13 - 15980950q^-12 - 9641991q^-11 + 2050425q^-10 + 12561147q^-9 + 15997522q^-8 + 10346608q^-7 - 1103802q^-6 - 11896387q^-5 - 15942378q^-4 - 10871239q^-3 + 344203q^-2 + 11352146q^-1 + 15915633 + 11352146q + 344203q² - 10871239q³ - 15942378q⁴ - 11896387q⁵ - 1103802q⁶ + 10346608q⁷ + 15997522q⁸ + 12561147q⁹ + 2050425q¹⁰ - 9641991q¹¹ - 15980950q¹² - 13335658q¹³ - 3272853q¹⁴ + 8612048q¹⁵ + 15752305q¹⁶ + 14138213q¹⁷ + 4783786q¹⁸ - 7142924q¹⁹ - 15135897q²⁰ - 14808343q²¹ - 6511733q²² + 5181766q²³ + 13970837q²⁴ + 15135646q²⁵ + 8283604q²⁶ - 2782605q²⁷ - 12155512q²⁸ - 14895676q²⁹ - 9843831q³⁰ + 121154q³¹ + 9700418q³² + 13915945q³³ + 10900762q³⁴ + 2515244q³⁵ - 6760636q³⁶ - 12142587q³⁷ - 11201786q³⁸ - 4775784q³⁹ + 3632710q⁴⁰ + 9681809q⁴¹ + 10610793q⁴² + 6335550q⁴³ - 696117q⁴⁴ - 6807311q⁴⁵ - 9173314q⁴⁶ - 6984275q⁴⁷ - 1670439q⁴⁸ + 3902842q⁴⁹ + 7115131q⁵⁰ + 6697142q⁵¹ + 3202185q⁵² - 1364682q⁵³ - 4799031q⁵⁴ - 5650023q⁵⁵ - 3814742q⁵⁶ - 502842q⁵⁷ + 2617311q⁵⁸ + 4160778q⁵⁹ + 3625400q⁶⁰ + 1573715q⁶¹ - 884016q⁶² - 2597945q⁶³ - 2902350q⁶⁴ - 1909001q⁶⁵ - 240851q⁶⁶ + 1265562q⁶⁷ + 1964892q⁶⁸ + 1714946q⁶⁹ + 773753q⁷⁰ - 333822q⁷¹ - 1089251q⁷² - 1254288q⁷³ - 857942q⁷⁴ - 173905q⁷⁵ + 439152q⁷⁶ + 753321q⁷⁷ + 689017q⁷⁸ + 349552q⁷⁹ - 55497q⁸⁰ - 356501q⁸¹ - 443178q⁸² - 325147q⁸³ - 106363q⁸⁴ + 109054q⁸⁵ + 228198q⁸⁶ + 223614q⁸⁷ + 133531q⁸⁸ + 7781q⁸⁹ - 89098q⁹⁰ - 122513q⁹¹ - 100446q⁹² - 40973q⁹³ + 18370q⁹⁴ + 52468q⁹⁵ + 58407q⁹⁶ + 37057q⁹⁷ + 6677q⁹⁸ - 16520q⁹⁹ - 27507q¹⁰⁰ - 22433q¹⁰¹ - 9940q¹⁰² + 1633q¹⁰³ + 10245q¹⁰⁴ + 11157q¹⁰⁵ + 7114q¹⁰⁶ + 1813q¹⁰⁷ - 3310q¹⁰⁸ - 4454q¹⁰⁹ - 3318q¹¹⁰ - 1739q¹¹¹ + 483q¹¹² + 1474q¹¹³ + 1554q¹¹⁴ + 1078q¹¹⁵ - 142q¹¹⁶ - 518q¹¹⁷ - 411q¹¹⁸ - 385q¹¹⁹ - 72q¹²⁰ + 35q¹²¹ + 163q¹²² + 242q¹²³ - 8q¹²⁴ - 69q¹²⁵ - 23q¹²⁶ - 27q¹²⁷ + 8q¹²⁸ - 24q¹²⁹ - 6q¹³⁰ + 43q¹³¹ - 2q¹³² - 14q¹³³ - q¹³⁴ + 9q¹³⁶ - 6q¹³⁷ - 3q¹³⁸ + 4q¹³⁹ - q¹⁴⁰

Computer Talk. The data above can be recomputed by Mathematica using the package KnotTheory`. Following setup, the sample Mathematica session below reproduces most of the above data (Mathematica system prompts in blue, human input in red, Mathematica output in black):

In[1]:=

<< KnotTheory`

Loading KnotTheory` (version of August 30, 2005, 10:15:35)...

In[2]:=
PD[Knot[10, 118]]

Out[2]=
PD[X[6, 2, 7, 1], X[18, 6, 19, 5], X[20, 13, 1, 14], X[12, 19, 13, 20], > X[14, 7, 15, 8], X[8, 3, 9, 4], X[2, 16, 3, 15], X[10, 18, 11, 17], > X[16, 10, 17, 9], X[4, 11, 5, 12]]

In[3]:=
GaussCode[Knot[10, 118]]

Out[3]=
GaussCode[1, -7, 6, -10, 2, -1, 5, -6, 9, -8, 10, -4, 3, -5, 7, -9, 8, -2, 4, > -3]

In[4]:=
DTCode[Knot[10, 118]]

Out[4]=
DTCode[6, 8, 18, 14, 16, 4, 20, 2, 10, 12]

In[5]:=
br = BR[Knot[10, 118]]

Out[5]=
BR[3, {1, 1, -2, 1, -2, 1, -2, -2, 1, -2}]

In[6]:=
{First[br], Crossings[br]}

Out[6]=
{3, 10}

In[7]:=
BraidIndex[Knot[10, 118]]

Out[7]=
3

In[8]:=
Show[DrawMorseLink[Knot[10, 118]]]

Out[8]=
-Graphics-

In[9]:=
#[Knot[10, 118]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}

Out[9]=
{NegativeAmphicheiral, 1, 4, 3, NotAvailable, 1}

In[10]:=
alex = Alexander[Knot[10, 118]][t]

Out[10]=
-4 5 12 19 2 3 4 23 + t - -- + -- - -- - 19 t + 12 t - 5 t + t 3 2 t t t

In[11]:=
Conway[Knot[10, 118]][z]

Out[11]=
4 6 8 1 + 2 z + 3 z + z

In[12]:=
Select[AllKnots[], (alex === Alexander[#][t])&]

Out[12]=
{Knot[10, 118], Knot[11, Alternating, 257]}

In[13]:=
{KnotDet[Knot[10, 118]], KnotSignature[Knot[10, 118]]}

Out[13]=
{97, 0}

In[14]:=
Jones[Knot[10, 118]][q]

Out[14]=
-5 4 8 12 15 2 3 4 5 17 - q + -- - -- + -- - -- - 15 q + 12 q - 8 q + 4 q - q 4 3 2 q q q q

In[15]:=
Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&]

Out[15]=
{Knot[10, 118]}

In[16]:=
A2Invariant[Knot[10, 118]][q]

Out[16]=
-14 2 2 2 2 4 2 4 8 10 12 14 -3 - q + --- - --- + -- - -- + -- + 4 q - 2 q + 2 q - 2 q + 2 q - q 12 10 8 4 2 q q q q q

In[17]:=
HOMFLYPT[Knot[10, 118]][a, z]

Out[17]=
2 4 6 2 2 z 2 2 4 3 z 2 4 6 z 2 6 8 1 + 4 z - ---- - 2 a z + 8 z - ---- - 3 a z + 5 z - -- - a z + z 2 2 2 a a a

In[18]:=
Kauffman[Knot[10, 118]][a, z]

Out[18]=
2 2 3 3 z 3 z 3 2 z 2 z 2 2 4 2 z 5 z 1 - -- - --- - 3 a z - a z - 6 z + -- - ---- - 2 a z + a z - -- + ---- + 3 a 4 2 5 3 a a a a a 3 4 4 15 z 3 3 3 5 3 4 6 z 6 z 2 4 > ----- + 15 a z + 5 a z - a z + 24 z - ---- + ---- + 6 a z - a 4 2 a a 5 5 5 6 4 4 z 12 z 20 z 5 3 5 5 5 6 4 z > 6 a z + -- - ----- - ----- - 20 a z - 12 a z + a z - 30 z + ---- - 5 3 a 4 a a a 6 7 7 11 z 2 6 4 6 7 z 6 z 7 3 7 8 > ----- - 11 a z + 4 a z + ---- + ---- + 6 a z + 7 a z + 14 z + 2 3 a a a 8 9 7 z 2 8 3 z 9 > ---- + 7 a z + ---- + 3 a z 2 a a

In[19]:=
{Vassiliev[2][Knot[10, 118]], Vassiliev[3][Knot[10, 118]]}

Out[19]=
{0, 0}

In[20]:=
Kh[Knot[10, 118]][q, t]

Out[20]=
9 1 3 1 5 3 7 5 8 7 - + 9 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + ---- + --- + q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 3 q t q t q t q t q t q t q t q t q t 3 3 2 5 2 5 3 7 3 7 4 9 4 > 7 q t + 8 q t + 5 q t + 7 q t + 3 q t + 5 q t + q t + 3 q t + 11 5 > q t

In[21]:=
ColouredJones[Knot[10, 118], 2][q]

Out[21]=
-15 4 3 11 27 8 52 76 8 130 122 55 241 + q - --- + --- + --- - --- + --- + -- - -- - -- + --- - --- - -- + 14 13 12 11 10 9 8 7 6 5 4 q q q q q q q q q q q 208 134 107 2 3 4 5 6 > --- - --- - --- - 107 q - 134 q + 208 q - 55 q - 122 q + 130 q - 3 2 q q q 7 8 9 10 11 12 13 14 15 > 8 q - 76 q + 52 q + 8 q - 27 q + 11 q + 3 q - 4 q + q

Dror Bar-Natan: The Knot Atlas: The Rolfsen Knot Table: The Knot 10₁₁₈

10₁₁₇
10₁₁₉

n	Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2	q^-15 - 4q^-14 + 3q^-13 + 11q^-12 - 27q^-11 + 8q^-10 + 52q^-9 - 76q^-8 - 8q^-7 + 130q^-6 - 122q^-5 - 55q^-4 + 208q^-3 - 134q^-2 - 107q^-1 + 241 - 107q - 134q² + 208q³ - 55q⁴ - 122q⁵ + 130q⁶ - 8q⁷ - 76q⁸ + 52q⁹ + 8q¹⁰ - 27q¹¹ + 11q¹² + 3q¹³ - 4q¹⁴ + q¹⁵
3	- q^-30 + 4q^-29 - 3q^-28 - 6q^-27 + 4q^-26 + 18q^-25 - 9q^-24 - 48q^-23 + 21q^-22 + 99q^-21 - 14q^-20 - 194q^-19 - 26q^-18 + 323q^-17 + 129q^-16 - 466q^-15 - 307q^-14 + 582q^-13 + 562q^-12 - 650q^-11 - 851q^-10 + 639q^-9 + 1148q^-8 - 565q^-7 - 1402q^-6 + 430q^-5 + 1603q^-4 - 274q^-3 - 1714q^-2 + 84q^-1 + 1769 + 84q - 1714q² - 274q³ + 1603q⁴ + 430q⁵ - 1402q⁶ - 565q⁷ + 1148q⁸ + 639q⁹ - 851q¹⁰ - 650q¹¹ + 562q¹² + 582q¹³ - 307q¹⁴ - 466q¹⁵ + 129q¹⁶ + 323q¹⁷ - 26q¹⁸ - 194q¹⁹ - 14q²⁰ + 99q²¹ + 21q²² - 48q²³ - 9q²⁴ + 18q²⁵ + 4q²⁶ - 6q²⁷ - 3q²⁸ + 4q²⁹ - q³⁰
4	q^-50 - 4q^-49 + 3q^-48 + 6q^-47 - 9q^-46 + 5q^-45 - 17q^-44 + 22q^-43 + 31q^-42 - 60q^-41 - 4q^-40 - 61q^-39 + 131q^-38 + 193q^-37 - 192q^-36 - 199q^-35 - 372q^-34 + 386q^-33 + 907q^-32 - 7q^-31 - 645q^-30 - 1686q^-29 + 78q^-28 + 2318q^-27 + 1584q^-26 - 286q^-25 - 4171q^-24 - 2229q^-23 + 2995q^-22 + 4722q^-21 + 2593q^-20 - 6078q^-19 - 6548q^-18 + 1037q^-17 + 7450q^-16 + 7776q^-15 - 5461q^-14 - 10670q^-13 - 3245q^-12 + 7881q^-11 + 12898q^-10 - 2626q^-9 - 12675q^-8 - 7693q^-7 + 6233q^-6 + 16074q^-5 + 739q^-4 - 12520q^-3 - 10838q^-2 + 3699q^-1 + 17069 + 3699q - 10838q² - 12520q³ + 739q⁴ + 16074q⁵ + 6233q⁶ - 7693q⁷ - 12675q⁸ - 2626q⁹ + 12898q¹⁰ + 7881q¹¹ - 3245q¹² - 10670q¹³ - 5461q¹⁴ + 7776q¹⁵ + 7450q¹⁶ + 1037q¹⁷ - 6548q¹⁸ - 6078q¹⁹ + 2593q²⁰ + 4722q²¹ + 2995q²² - 2229q²³ - 4171q²⁴ - 286q²⁵ + 1584q²⁶ + 2318q²⁷ + 78q²⁸ - 1686q²⁹ - 645q³⁰ - 7q³¹ + 907q³² + 386q³³ - 372q³⁴ - 199q³⁵ - 192q³⁶ + 193q³⁷ + 131q³⁸ - 61q³⁹ - 4q⁴⁰ - 60q⁴¹ + 31q⁴² + 22q⁴³ - 17q⁴⁴ + 5q⁴⁵ - 9q⁴⁶ + 6q⁴⁷ + 3q⁴⁸ - 4q⁴⁹ + q⁵⁰
5	- q^-75 + 4q^-74 - 3q^-73 - 6q^-72 + 9q^-71 - 6q^-69 + 4q^-68 - 5q^-67 - 9q^-66 + 37q^-65 + 29q^-64 - 48q^-63 - 83q^-62 - 68q^-61 + 46q^-60 + 244q^-59 + 301q^-58 - 24q^-57 - 573q^-56 - 787q^-55 - 287q^-54 + 875q^-53 + 1843q^-52 + 1364q^-51 - 921q^-50 - 3428q^-49 - 3602q^-48 - 259q^-47 + 4964q^-46 + 7568q^-45 + 3700q^-44 - 5394q^-43 - 12667q^-42 - 10365q^-41 + 2685q^-40 + 17588q^-39 + 20463q^-38 + 4813q^-37 - 19877q^-36 - 32656q^-35 - 18124q^-34 + 16897q^-33 + 44345q^-32 + 36630q^-31 - 6744q^-30 - 52443q^-29 - 57942q^-28 - 10715q^-27 + 54076q^-26 + 78732q^-25 + 34017q^-24 - 48179q^-23 - 95785q^-22 - 59901q^-21 + 35233q^-20 + 106740q^-19 + 85226q^-18 - 17417q^-17 - 111131q^-16 - 107011q^-15 - 2543q^-14 + 109646q^-13 + 123904q^-12 + 22010q^-11 - 104034q^-10 - 135442q^-9 - 39509q^-8 + 96005q^-7 + 142679q^-6 + 54100q^-5 - 86907q^-4 - 146180q^-3 - 66504q^-2 + 77050q^-1 + 147507 + 77050q - 66504q² - 146180q³ - 86907q⁴ + 54100q⁵ + 142679q⁶ + 96005q⁷ - 39509q⁸ - 135442q⁹ - 104034q¹⁰ + 22010q¹¹ + 123904q¹² + 109646q¹³ - 2543q¹⁴ - 107011q¹⁵ - 111131q¹⁶ - 17417q¹⁷ + 85226q¹⁸ + 106740q¹⁹ + 35233q²⁰ - 59901q²¹ - 95785q²² - 48179q²³ + 34017q²⁴ + 78732q²⁵ + 54076q²⁶ - 10715q²⁷ - 57942q²⁸ - 52443q²⁹ - 6744q³⁰ + 36630q³¹ + 44345q³² + 16897q³³ - 18124q³⁴ - 32656q³⁵ - 19877q³⁶ + 4813q³⁷ + 20463q³⁸ + 17588q³⁹ + 2685q⁴⁰ - 10365q⁴¹ - 12667q⁴² - 5394q⁴³ + 3700q⁴⁴ + 7568q⁴⁵ + 4964q⁴⁶ - 259q⁴⁷ - 3602q⁴⁸ - 3428q⁴⁹ - 921q⁵⁰ + 1364q⁵¹ + 1843q⁵² + 875q⁵³ - 287q⁵⁴ - 787q⁵⁵ - 573q⁵⁶ - 24q⁵⁷ + 301q⁵⁸ + 244q⁵⁹ + 46q⁶⁰ - 68q⁶¹ - 83q⁶² - 48q⁶³ + 29q⁶⁴ + 37q⁶⁵ - 9q⁶⁶ - 5q⁶⁷ + 4q⁶⁸ - 6q⁶⁹ + 9q⁷¹ - 6q⁷² - 3q⁷³ + 4q⁷⁴ - q⁷⁵
6	q^-105 - 4q^-104 + 3q^-103 + 6q^-102 - 9q^-101 + q^-99 + 19q^-98 - 21q^-97 - 17q^-96 + 32q^-95 - 45q^-94 + 8q^-93 + 50q^-92 + 128q^-91 - 41q^-90 - 167q^-89 - 62q^-88 - 286q^-87 - 16q^-86 + 387q^-85 + 900q^-84 + 404q^-83 - 424q^-82 - 881q^-81 - 2094q^-80 - 1401q^-79 + 650q^-78 + 3938q^-77 + 4458q^-76 + 2396q^-75 - 1204q^-74 - 8305q^-73 - 10766q^-72 - 6703q^-71 + 5801q^-70 + 16461q^-69 + 20757q^-68 + 14405q^-67 - 9709q^-66 - 33262q^-65 - 42976q^-64 - 22056q^-63 + 15948q^-62 + 58065q^-61 + 77950q^-60 + 42156q^-59 - 29551q^-58 - 104768q^-57 - 122544q^-56 - 71254q^-55 + 47281q^-54 + 171007q^-53 + 198422q^-52 + 103304q^-51 - 89064q^-50 - 253004q^-49 - 297475q^-48 - 141664q^-47 + 149780q^-46 + 383153q^-45 + 408243q^-44 + 154486q^-43 - 230153q^-42 - 546632q^-41 - 530354q^-40 - 143910q^-39 + 380359q^-38 + 726609q^-37 + 615539q^-36 + 96521q^-35 - 581428q^-34 - 920446q^-33 - 660120q^-32 + 60354q^-31 + 813628q^-30 + 1064305q^-29 + 635918q^-28 - 301929q^-27 - 1072972q^-26 - 1148980q^-25 - 451384q^-24 + 602132q^-23 + 1278685q^-22 + 1132696q^-21 + 144123q^-20 - 950647q^-19 - 1413224q^-18 - 910924q^-17 + 247709q^-16 + 1245688q^-15 + 1420940q^-14 + 538462q^-13 - 703247q^-12 - 1458570q^-11 - 1189250q^-10 - 66498q^-9 + 1100658q^-8 + 1522082q^-7 + 790633q^-6 - 474803q^-5 - 1403113q^-4 - 1322934q^-3 - 286649q^-2 + 950870q^-1 + 1538859 + 950870q - 286649q² - 1322934q³ - 1403113q⁴ - 474803q⁵ + 790633q⁶ + 1522082q⁷ + 1100658q⁸ - 66498q⁹ - 1189250q¹⁰ - 1458570q¹¹ - 703247q¹² + 538462q¹³ + 1420940q¹⁴ + 1245688q¹⁵ + 247709q¹⁶ - 910924q¹⁷ - 1413224q¹⁸ - 950647q¹⁹ + 144123q²⁰ + 1132696q²¹ + 1278685q²² + 602132q²³ - 451384q²⁴ - 1148980q²⁵ - 1072972q²⁶ - 301929q²⁷ + 635918q²⁸ + 1064305q²⁹ + 813628q³⁰ + 60354q³¹ - 660120q³² - 920446q³³ - 581428q³⁴ + 96521q³⁵ + 615539q³⁶ + 726609q³⁷ + 380359q³⁸ - 143910q³⁹ - 530354q⁴⁰ - 546632q⁴¹ - 230153q⁴² + 154486q⁴³ + 408243q⁴⁴ + 383153q⁴⁵ + 149780q⁴⁶ - 141664q⁴⁷ - 297475q⁴⁸ - 253004q⁴⁹ - 89064q⁵⁰ + 103304q⁵¹ + 198422q⁵² + 171007q⁵³ + 47281q⁵⁴ - 71254q⁵⁵ - 122544q⁵⁶ - 104768q⁵⁷ - 29551q⁵⁸ + 42156q⁵⁹ + 77950q⁶⁰ + 58065q⁶¹ + 15948q⁶² - 22056q⁶³ - 42976q⁶⁴ - 33262q⁶⁵ - 9709q⁶⁶ + 14405q⁶⁷ + 20757q⁶⁸ + 16461q⁶⁹ + 5801q⁷⁰ - 6703q⁷¹ - 10766q⁷² - 8305q⁷³ - 1204q⁷⁴ + 2396q⁷⁵ + 4458q⁷⁶ + 3938q⁷⁷ + 650q⁷⁸ - 1401q⁷⁹ - 2094q⁸⁰ - 881q⁸¹ - 424q⁸² + 404q⁸³ + 900q⁸⁴ + 387q⁸⁵ - 16q⁸⁶ - 286q⁸⁷ - 62q⁸⁸ - 167q⁸⁹ - 41q⁹⁰ + 128q⁹¹ + 50q⁹² + 8q⁹³ - 45q⁹⁴ + 32q⁹⁵ - 17q⁹⁶ - 21q⁹⁷ + 19q⁹⁸ + q⁹⁹ - 9q¹⁰¹ + 6q¹⁰² + 3q¹⁰³ - 4q¹⁰⁴ + q¹⁰⁵
7	- q^-140 + 4q^-139 - 3q^-138 - 6q^-137 + 9q^-136 - q^-134 - 14q^-133 - 2q^-132 + 43q^-131 - 6q^-130 - 24q^-129 + 8q^-128 - 27q^-127 - 23q^-126 - 69q^-125 - 8q^-124 + 242q^-123 + 163q^-122 + 35q^-121 - 72q^-120 - 385q^-119 - 411q^-118 - 518q^-117 - 142q^-116 + 1078q^-115 + 1554q^-114 + 1474q^-113 + 483q^-112 - 1739q^-111 - 3318q^-110 - 4454q^-109 - 3310q^-108 + 1813q^-107 + 7114q^-106 + 11157q^-105 + 10245q^-104 + 1633q^-103 - 9940q^-102 - 22433q^-101 - 27507q^-100 - 16520q^-99 + 6677q^-98 + 37057q^-97 + 58407q^-96 + 52468q^-95 + 18370q^-94 - 40973q^-93 - 100446q^-92 - 122513q^-91 - 89098q^-90 + 7781q^-89 + 133531q^-88 + 223614q^-87 + 228198q^-86 + 109054q^-85 - 106363q^-84 - 325147q^-83 - 443178q^-82 - 356501q^-81 - 55497q^-80 + 349552q^-79 + 689017q^-78 + 753321q^-77 + 439152q^-76 - 173905q^-75 - 857942q^-74 - 1254288q^-73 - 1089251q^-72 - 333822q^-71 + 773753q^-70 + 1714946q^-69 + 1964892q^-68 + 1265562q^-67 - 240851q^-66 - 1909001q^-65 - 2902350q^-64 - 2597945q^-63 - 884016q^-62 + 1573715q^-61 + 3625400q^-60 + 4160778q^-59 + 2617311q^-58 - 502842q^-57 - 3814742q^-56 - 5650023q^-55 - 4799031q^-54 - 1364682q^-53 + 3202185q^-52 + 6697142q^-51 + 7115131q^-50 + 3902842q^-49 - 1670439q^-48 - 6984275q^-47 - 9173314q^-46 - 6807311q^-45 - 696117q^-44 + 6335550q^-43 + 10610793q^-42 + 9681809q^-41 + 3632710q^-40 - 4775784q^-39 - 11201786q^-38 - 12142587q^-37 - 6760636q^-36 + 2515244q^-35 + 10900762q^-34 + 13915945q^-33 + 9700418q^-32 + 121154q^-31 - 9843831q^-30 - 14895676q^-29 - 12155512q^-28 - 2782605q^-27 + 8283604q^-26 + 15135646q^-25 + 13970837q^-24 + 5181766q^-23 - 6511733q^-22 - 14808343q^-21 - 15135897q^-20 - 7142924q^-19 + 4783786q^-18 + 14138213q^-17 + 15752305q^-16 + 8612048q^-15 - 3272853q^-14 - 13335658q^-13 - 15980950q^-12 - 9641991q^-11 + 2050425q^-10 + 12561147q^-9 + 15997522q^-8 + 10346608q^-7 - 1103802q^-6 - 11896387q^-5 - 15942378q^-4 - 10871239q^-3 + 344203q^-2 + 11352146q^-1 + 15915633 + 11352146q + 344203q² - 10871239q³ - 15942378q⁴ - 11896387q⁵ - 1103802q⁶ + 10346608q⁷ + 15997522q⁸ + 12561147q⁹ + 2050425q¹⁰ - 9641991q¹¹ - 15980950q¹² - 13335658q¹³ - 3272853q¹⁴ + 8612048q¹⁵ + 15752305q¹⁶ + 14138213q¹⁷ + 4783786q¹⁸ - 7142924q¹⁹ - 15135897q²⁰ - 14808343q²¹ - 6511733q²² + 5181766q²³ + 13970837q²⁴ + 15135646q²⁵ + 8283604q²⁶ - 2782605q²⁷ - 12155512q²⁸ - 14895676q²⁹ - 9843831q³⁰ + 121154q³¹ + 9700418q³² + 13915945q³³ + 10900762q³⁴ + 2515244q³⁵ - 6760636q³⁶ - 12142587q³⁷ - 11201786q³⁸ - 4775784q³⁹ + 3632710q⁴⁰ + 9681809q⁴¹ + 10610793q⁴² + 6335550q⁴³ - 696117q⁴⁴ - 6807311q⁴⁵ - 9173314q⁴⁶ - 6984275q⁴⁷ - 1670439q⁴⁸ + 3902842q⁴⁹ + 7115131q⁵⁰ + 6697142q⁵¹ + 3202185q⁵² - 1364682q⁵³ - 4799031q⁵⁴ - 5650023q⁵⁵ - 3814742q⁵⁶ - 502842q⁵⁷ + 2617311q⁵⁸ + 4160778q⁵⁹ + 3625400q⁶⁰ + 1573715q⁶¹ - 884016q⁶² - 2597945q⁶³ - 2902350q⁶⁴ - 1909001q⁶⁵ - 240851q⁶⁶ + 1265562q⁶⁷ + 1964892q⁶⁸ + 1714946q⁶⁹ + 773753q⁷⁰ - 333822q⁷¹ - 1089251q⁷² - 1254288q⁷³ - 857942q⁷⁴ - 173905q⁷⁵ + 439152q⁷⁶ + 753321q⁷⁷ + 689017q⁷⁸ + 349552q⁷⁹ - 55497q⁸⁰ - 356501q⁸¹ - 443178q⁸² - 325147q⁸³ - 106363q⁸⁴ + 109054q⁸⁵ + 228198q⁸⁶ + 223614q⁸⁷ + 133531q⁸⁸ + 7781q⁸⁹ - 89098q⁹⁰ - 122513q⁹¹ - 100446q⁹² - 40973q⁹³ + 18370q⁹⁴ + 52468q⁹⁵ + 58407q⁹⁶ + 37057q⁹⁷ + 6677q⁹⁸ - 16520q⁹⁹ - 27507q¹⁰⁰ - 22433q¹⁰¹ - 9940q¹⁰² + 1633q¹⁰³ + 10245q¹⁰⁴ + 11157q¹⁰⁵ + 7114q¹⁰⁶ + 1813q¹⁰⁷ - 3310q¹⁰⁸ - 4454q¹⁰⁹ - 3318q¹¹⁰ - 1739q¹¹¹ + 483q¹¹² + 1474q¹¹³ + 1554q¹¹⁴ + 1078q¹¹⁵ - 142q¹¹⁶ - 518q¹¹⁷ - 411q¹¹⁸ - 385q¹¹⁹ - 72q¹²⁰ + 35q¹²¹ + 163q¹²² + 242q¹²³ - 8q¹²⁴ - 69q¹²⁵ - 23q¹²⁶ - 27q¹²⁷ + 8q¹²⁸ - 24q¹²⁹ - 6q¹³⁰ + 43q¹³¹ - 2q¹³² - 14q¹³³ - q¹³⁴ + 9q¹³⁶ - 6q¹³⁷ - 3q¹³⁸ + 4q¹³⁹ - q¹⁴⁰

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 30, 2005, 10:15:35)...
In[2]:=	PD[Knot[10, 118]]
Out[2]=	PD[X[6, 2, 7, 1], X[18, 6, 19, 5], X[20, 13, 1, 14], X[12, 19, 13, 20], > X[14, 7, 15, 8], X[8, 3, 9, 4], X[2, 16, 3, 15], X[10, 18, 11, 17], > X[16, 10, 17, 9], X[4, 11, 5, 12]]
In[3]:=	GaussCode[Knot[10, 118]]
Out[3]=	GaussCode[1, -7, 6, -10, 2, -1, 5, -6, 9, -8, 10, -4, 3, -5, 7, -9, 8, -2, 4, > -3]
In[4]:=	DTCode[Knot[10, 118]]
Out[4]=	DTCode[6, 8, 18, 14, 16, 4, 20, 2, 10, 12]
In[5]:=	br = BR[Knot[10, 118]]
Out[5]=	BR[3, {1, 1, -2, 1, -2, 1, -2, -2, 1, -2}]
In[6]:=	{First[br], Crossings[br]}
Out[6]=	{3, 10}
In[7]:=	BraidIndex[Knot[10, 118]]
Out[7]=	3
In[8]:=	Show[DrawMorseLink[Knot[10, 118]]]

Out[8]=	-Graphics-
In[9]:=	#[Knot[10, 118]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}
Out[9]=	{NegativeAmphicheiral, 1, 4, 3, NotAvailable, 1}
In[10]:=	alex = Alexander[Knot[10, 118]][t]
Out[10]=	-4 5 12 19 2 3 4 23 + t - -- + -- - -- - 19 t + 12 t - 5 t + t 3 2 t t t
In[11]:=	Conway[Knot[10, 118]][z]
Out[11]=	4 6 8 1 + 2 z + 3 z + z
In[12]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]=	{Knot[10, 118], Knot[11, Alternating, 257]}
In[13]:=	{KnotDet[Knot[10, 118]], KnotSignature[Knot[10, 118]]}
Out[13]=	{97, 0}
In[14]:=	Jones[Knot[10, 118]][q]
Out[14]=	-5 4 8 12 15 2 3 4 5 17 - q + -- - -- + -- - -- - 15 q + 12 q - 8 q + 4 q - q 4 3 2 q q q q
In[15]:=	Select[AllKnots[], (J === Jones[#][q] \|\| (J /. q-> 1/q) === Jones[#][q])&]
Out[15]=	{Knot[10, 118]}
In[16]:=	A2Invariant[Knot[10, 118]][q]
Out[16]=	-14 2 2 2 2 4 2 4 8 10 12 14 -3 - q + --- - --- + -- - -- + -- + 4 q - 2 q + 2 q - 2 q + 2 q - q 12 10 8 4 2 q q q q q
In[17]:=	HOMFLYPT[Knot[10, 118]][a, z]
Out[17]=	2 4 6 2 2 z 2 2 4 3 z 2 4 6 z 2 6 8 1 + 4 z - ---- - 2 a z + 8 z - ---- - 3 a z + 5 z - -- - a z + z 2 2 2 a a a
In[18]:=	Kauffman[Knot[10, 118]][a, z]
Out[18]=	2 2 3 3 z 3 z 3 2 z 2 z 2 2 4 2 z 5 z 1 - -- - --- - 3 a z - a z - 6 z + -- - ---- - 2 a z + a z - -- + ---- + 3 a 4 2 5 3 a a a a a 3 4 4 15 z 3 3 3 5 3 4 6 z 6 z 2 4 > ----- + 15 a z + 5 a z - a z + 24 z - ---- + ---- + 6 a z - a 4 2 a a 5 5 5 6 4 4 z 12 z 20 z 5 3 5 5 5 6 4 z > 6 a z + -- - ----- - ----- - 20 a z - 12 a z + a z - 30 z + ---- - 5 3 a 4 a a a 6 7 7 11 z 2 6 4 6 7 z 6 z 7 3 7 8 > ----- - 11 a z + 4 a z + ---- + ---- + 6 a z + 7 a z + 14 z + 2 3 a a a 8 9 7 z 2 8 3 z 9 > ---- + 7 a z + ---- + 3 a z 2 a a
In[19]:=	{Vassiliev[2][Knot[10, 118]], Vassiliev[3][Knot[10, 118]]}
Out[19]=	{0, 0}
In[20]:=	Kh[Knot[10, 118]][q, t]
Out[20]=	9 1 3 1 5 3 7 5 8 7 - + 9 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + ---- + --- + q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 3 q t q t q t q t q t q t q t q t q t 3 3 2 5 2 5 3 7 3 7 4 9 4 > 7 q t + 8 q t + 5 q t + 7 q t + 3 q t + 5 q t + q t + 3 q t + 11 5 > q t
In[21]:=	ColouredJones[Knot[10, 118], 2][q]
Out[21]=	-15 4 3 11 27 8 52 76 8 130 122 55 241 + q - --- + --- + --- - --- + --- + -- - -- - -- + --- - --- - -- + 14 13 12 11 10 9 8 7 6 5 4 q q q q q q q q q q q 208 134 107 2 3 4 5 6 > --- - --- - --- - 107 q - 134 q + 208 q - 55 q - 122 q + 130 q - 3 2 q q q 7 8 9 10 11 12 13 14 15 > 8 q - 76 q + 52 q + 8 q - 27 q + 11 q + 3 q - 4 q + q

The Alternating Knot 10118

The Alternating Knot 10₁₁₈