The Alternating Knot 10₉₄

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Acknowledgement

KnotPlot

PD Presentation: X₆₂₇₁ X₂₈₃₇ X_18,12,19,11 X_14,5,15,6 X_20,14,1,13 X_8,15,9,16 X_10,4,11,3 X_16,9,17,10 X_4,17,5,18 X_12,20,13,19

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

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

Chiral 2 4 3 / NotAvailable 1

Alexander Polynomial: - t^-4 + 4t^-3 - 9t^-2 + 14t^-1 - 15 + 14t - 9t² + 4t³ - t⁴

Conway Polynomial: 1 - 2z² - 5z⁴ - 4z⁶ - z⁸

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

Determinant and Signature: {71, 2}

Jones Polynomial: q^-3 - 3q^-2 + 6q^-1 - 8 + 11q - 12q² + 11q³ - 9q⁴ + 6q⁵ - 3q⁶ + q⁷

Other knots (up to mirrors) with the same Jones Polynomial: {10₄₁, ...}

A2 (sl(3)) Invariant: q^-8 - q^-6 + 2q^-4 + 1 + 2q² - 3q⁴ + 2q⁶ - 3q⁸ + q¹⁰ - q¹⁴ + 2q¹⁶ - q¹⁸ + q²⁰

HOMFLY-PT Polynomial: 2a^-4 + 5a^-4z² + 4a^-4z⁴ + a^-4z⁶ - 4a^-2 - 12a^-2z² - 13a^-2z⁴ - 6a^-2z⁶ - a^-2z⁸ + 3 + 5z² + 4z⁴ + z⁶

Kauffman Polynomial: - a^-8z² + a^-8z⁴ - 3a^-7z³ + 3a^-7z⁵ + 2a^-6z² - 6a^-6z⁴ + 5a^-6z⁶ - 3a^-5z + 9a^-5z³ - 10a^-5z⁵ + 6a^-5z⁷ + 2a^-4 - 6a^-4z² + 10a^-4z⁴ - 9a^-4z⁶ + 5a^-4z⁸ - 5a^-3z + 16a^-3z³ - 15a^-3z⁵ + 3a^-3z⁷ + 2a^-3z⁹ + 4a^-2 - 18a^-2z² + 31a^-2z⁴ - 27a^-2z⁶ + 9a^-2z⁸ - 3a^-1z + 10a^-1z³ - 11a^-1z⁵ + 2a^-1z⁹ + 3 - 7z² + 11z⁴ - 12z⁶ + 4z⁸ - az + 6az³ - 9az⁵ + 3az⁷ + 2a²z² - 3a²z⁴ + a²z⁶

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

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=2 is the signature of 10₉₄. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.)

t^rq^j r = -4 r = -3 r = -2 r = -1 r = 0 r = 1 r = 2 r = 3 r = 4 r = 5 r = 6

j = 15 1

j = 13 2

j = 11 4 1

j = 9 5 2

j = 7 6 4

j = 5 6 5

j = 3 5 6

j = 1 4 7

j = -1 2 4

j = -3 1 4

j = -5 2

j = -7 1

n Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2 q^-10 - 3q^-9 + q^-8 + 10q^-7 - 15q^-6 - 6q^-5 + 36q^-4 - 27q^-3 - 31q^-2 + 70q^-1 - 24 - 67q + 94q² - 9q³ - 97q⁴ + 98q⁵ + 11q⁶ - 104q⁷ + 79q⁸ + 23q⁹ - 81q¹⁰ + 46q¹¹ + 20q¹² - 43q¹³ + 19q¹⁴ + 9q¹⁵ - 15q¹⁶ + 6q¹⁷ + 2q¹⁸ - 3q¹⁹ + q²⁰

3 q^-21 - 3q^-20 + q^-19 + 5q^-18 + 2q^-17 - 15q^-16 - 8q^-15 + 29q^-14 + 26q^-13 - 44q^-12 - 58q^-11 + 46q^-10 + 112q^-9 - 37q^-8 - 164q^-7 - 9q^-6 + 219q^-5 + 71q^-4 - 245q^-3 - 161q^-2 + 259q^-1 + 241 - 229q - 332q² + 197q³ + 395q⁴ - 137q⁵ - 456q⁶ + 81q⁷ + 492q⁸ - 18q⁹ - 509q¹⁰ - 46q¹¹ + 504q¹² + 102q¹³ - 469q¹⁴ - 148q¹⁵ + 406q¹⁶ + 176q¹⁷ - 321q¹⁸ - 182q¹⁹ + 231q²⁰ + 161q²¹ - 146q²² - 124q²³ + 81q²⁴ + 83q²⁵ - 43q²⁶ - 44q²⁷ + 21q²⁸ + 21q²⁹ - 14q³⁰ - 8q³¹ + 10q³² + 3q³³ - 7q³⁴ + 2q³⁶ + 2q³⁷ - 3q³⁸ + q³⁹

4 q^-36 - 3q^-35 + q^-34 + 5q^-33 - 3q^-32 + 2q^-31 - 18q^-30 + 4q^-29 + 32q^-28 + 2q^-27 + 9q^-26 - 88q^-25 - 34q^-24 + 93q^-23 + 80q^-22 + 113q^-21 - 214q^-20 - 228q^-19 + 34q^-18 + 194q^-17 + 492q^-16 - 152q^-15 - 501q^-14 - 361q^-13 - 5q^-12 + 990q^-11 + 348q^-10 - 383q^-9 - 871q^-8 - 782q^-7 + 1052q^-6 + 996q^-5 + 396q^-4 - 906q^-3 - 1778q^-2 + 412q^-1 + 1195 + 1471q - 259q² - 2417q³ - 568q⁴ + 793q⁵ + 2313q⁶ + 703q⁷ - 2550q⁸ - 1436q⁹ + 122q¹⁰ + 2781q¹¹ + 1582q¹² - 2381q¹³ - 2063q¹⁴ - 546q¹⁵ + 2954q¹⁶ + 2280q¹⁷ - 1987q¹⁸ - 2456q¹⁹ - 1206q²⁰ + 2758q²¹ + 2752q²² - 1261q²³ - 2418q²⁴ - 1809q²⁵ + 2000q²⁶ + 2750q²⁷ - 294q²⁸ - 1745q²⁹ - 2018q³⁰ + 874q³¹ + 2063q³² + 403q³³ - 698q³⁴ - 1566q³⁵ + 5q³⁶ + 1020q³⁷ + 473q³⁸ + 58q³⁹ - 786q⁴⁰ - 231q⁴¹ + 271q⁴² + 187q⁴³ + 235q⁴⁴ - 240q⁴⁵ - 112q⁴⁶ + 20q⁴⁷ - 7q⁴⁸ + 128q⁴⁹ - 49q⁵⁰ - 11q⁵¹ - 34q⁵³ + 39q⁵⁴ - 13q⁵⁵ + 5q⁵⁶ + 5q⁵⁷ - 13q⁵⁸ + 8q⁵⁹ - 4q⁶⁰ + 2q⁶¹ + 2q⁶² - 3q⁶³ + q⁶⁴

5 q^-55 - 3q^-54 + q^-53 + 5q^-52 - 3q^-51 - 3q^-50 - q^-49 - 6q^-48 + 6q^-47 + 27q^-46 + 6q^-45 - 29q^-44 - 39q^-43 - 41q^-42 + 19q^-41 + 113q^-40 + 130q^-39 - 174q^-37 - 277q^-36 - 169q^-35 + 186q^-34 + 511q^-33 + 478q^-32 - 13q^-31 - 678q^-30 - 957q^-29 - 467q^-28 + 592q^-27 + 1450q^-26 + 1298q^-25 - 65q^-24 - 1680q^-23 - 2232q^-22 - 1079q^-21 + 1266q^-20 + 3054q^-19 + 2604q^-18 - 73q^-17 - 3107q^-16 - 4181q^-15 - 2006q^-14 + 2223q^-13 + 5228q^-12 + 4425q^-11 - 84q^-10 - 5237q^-9 - 6808q^-8 - 2899q^-7 + 3926q^-6 + 8388q^-5 + 6417q^-4 - 1349q^-3 - 8940q^-2 - 9668q^-1 - 2169 + 8112q + 12432q² + 6090q³ - 6338q⁴ - 14137q⁵ - 9920q⁶ + 3680q⁷ + 15054q⁸ + 13335q⁹ - 886q¹⁰ - 15114q¹¹ - 16079q¹² - 1980q¹³ + 14765q¹⁴ + 18273q¹⁵ + 4472q¹⁶ - 14173q¹⁷ - 19936q¹⁸ - 6687q¹⁹ + 13516q²⁰ + 21309q²¹ + 8650q²² - 12816q²³ - 22459q²⁴ - 10514q²⁵ + 11921q²⁶ + 23334q²⁷ + 12469q²⁸ - 10608q²⁹ - 23833q³⁰ - 14466q³¹ + 8658q³² + 23618q³³ + 16382q³⁴ - 5971q³⁵ - 22400q³⁶ - 17892q³⁷ + 2694q³⁸ + 20004q³⁹ + 18567q⁴⁰ + 767q⁴¹ - 16463q⁴² - 18039q⁴³ - 3926q⁴⁴ + 12173q⁴⁵ + 16249q⁴⁶ + 6177q⁴⁷ - 7751q⁴⁸ - 13343q⁴⁹ - 7210q⁵⁰ + 3793q⁵¹ + 9896q⁵² + 7029q⁵³ - 867q⁵⁴ - 6507q⁵⁵ - 5879q⁵⁶ - 885q⁵⁷ + 3639q⁵⁸ + 4340q⁵⁹ + 1585q⁶⁰ - 1659q⁶¹ - 2787q⁶² - 1545q⁶³ + 467q⁶⁴ + 1559q⁶⁵ + 1191q⁶⁶ + 68q⁶⁷ - 753q⁶⁸ - 761q⁶⁹ - 218q⁷⁰ + 296q⁷¹ + 416q⁷² + 201q⁷³ - 76q⁷⁴ - 211q⁷⁵ - 136q⁷⁶ + 20q⁷⁷ + 81q⁷⁸ + 61q⁷⁹ + 22q⁸⁰ - 32q⁸¹ - 44q⁸² + 4q⁸³ + 12q⁸⁴ + 11q⁸⁶ - 11q⁸⁸ + 2q⁸⁹ + 4q⁹⁰ - 4q⁹¹ + 2q⁹² + 2q⁹³ - 3q⁹⁴ + q⁹⁵

6 q^-78 - 3q^-77 + q^-76 + 5q^-75 - 3q^-74 - 3q^-73 - 6q^-72 + 11q^-71 - 4q^-70 + q^-69 + 30q^-68 - 13q^-67 - 29q^-66 - 53q^-65 + 17q^-64 + 11q^-63 + 48q^-62 + 162q^-61 + 39q^-60 - 87q^-59 - 289q^-58 - 171q^-57 - 161q^-56 + 97q^-55 + 640q^-54 + 611q^-53 + 333q^-52 - 519q^-51 - 828q^-50 - 1343q^-49 - 917q^-48 + 722q^-47 + 1874q^-46 + 2474q^-45 + 1170q^-44 - 200q^-43 - 3105q^-42 - 4416q^-41 - 2675q^-40 + 490q^-39 + 4516q^-38 + 5829q^-37 + 5846q^-36 + 108q^-35 - 6138q^-34 - 9283q^-33 - 8158q^-32 - 1610q^-31 + 5761q^-30 + 14222q^-29 + 12409q^-28 + 4280q^-27 - 7232q^-26 - 16746q^-25 - 18002q^-24 - 10706q^-23 + 8596q^-22 + 21136q^-21 + 25233q^-20 + 15116q^-19 - 5167q^-18 - 26171q^-17 - 36810q^-16 - 20968q^-15 + 3772q^-14 + 32694q^-13 + 45216q^-12 + 33095q^-11 - 2967q^-10 - 44217q^-9 - 56203q^-8 - 41627q^-7 + 4740q^-6 + 52409q^-5 + 74828q^-4 + 48522q^-3 - 13942q^-2 - 66082q^-1 - 88427 - 50746q + 21863q² + 90405q³ + 99972q⁴ + 42040q⁵ - 40252q⁶ - 109818q⁷ - 105278q⁸ - 31451q⁹ + 73582q¹⁰ + 128048q¹¹ + 96351q¹² + 4767q¹³ - 102946q¹⁴ - 138997q¹⁵ - 82204q¹⁶ + 40951q¹⁷ + 132174q¹⁸ + 132448q¹⁹ + 46553q²⁰ - 83371q²¹ - 152588q²² - 116998q²³ + 11328q²⁴ + 125991q²⁵ + 151950q²⁶ + 75147q²⁷ - 66087q²⁸ - 157689q²⁹ - 138620q³⁰ - 9091q³¹ + 120705q³² + 165160q³³ + 95387q³⁴ - 53444q³⁵ - 162353q³⁶ - 157073q³⁷ - 27884q³⁸ + 114897q³⁹ + 177797q⁴⁰ + 117935q⁴¹ - 34928q⁴² - 161683q⁴³ - 176214q⁴⁴ - 56446q⁴⁵ + 95214q⁴⁶ + 181507q⁴⁷ + 144507q⁴⁸ + 1003q⁴⁹ - 139743q⁵⁰ - 183941q⁵¹ - 93242q⁵² + 50968q⁵³ + 158071q⁵⁴ + 158531q⁵⁵ + 48286q⁵⁶ - 87818q⁵⁷ - 160243q⁵⁸ - 116553q⁵⁹ - 6168q⁶⁰ + 101857q⁶¹ + 138724q⁶² + 80141q⁶³ - 23708q⁶⁴ - 103483q⁶⁵ - 104637q⁶⁶ - 45260q⁶⁷ + 36364q⁶⁸ + 87674q⁶⁹ + 75854q⁷⁰ + 19312q⁷¹ - 41443q⁷² - 64110q⁷³ - 48249q⁷⁴ - 5452q⁷⁵ + 35069q⁷⁶ + 45846q⁷⁷ + 27437q⁷⁸ - 4001q⁷⁹ - 24253q⁸⁰ - 28684q⁸¹ - 15195q⁸² + 5570q⁸³ + 17335q⁸⁴ + 16309q⁸⁵ + 5863q⁸⁶ - 3749q⁸⁷ - 10398q⁸⁸ - 9329q⁸⁹ - 2211q⁹⁰ + 3575q⁹¹ + 5717q⁹² + 3791q⁹³ + 1253q⁹⁴ - 2206q⁹⁵ - 3400q⁹⁶ - 1663q⁹⁷ + 89q⁹⁸ + 1275q⁹⁹ + 1192q¹⁰⁰ + 1025q¹⁰¹ - 187q¹⁰² - 929q¹⁰³ - 535q¹⁰⁴ - 186q¹⁰⁵ + 191q¹⁰⁶ + 213q¹⁰⁷ + 398q¹⁰⁸ + 49q¹⁰⁹ - 230q¹¹⁰ - 106q¹¹¹ - 67q¹¹² + 24q¹¹³ + 114q¹¹⁵ + 23q¹¹⁶ - 58q¹¹⁷ - 7q¹¹⁸ - 12q¹¹⁹ + 10q¹²⁰ - 16q¹²¹ + 24q¹²² + 6q¹²³ - 16q¹²⁴ + 4q¹²⁵ - 2q¹²⁶ + 4q¹²⁷ - 4q¹²⁸ + 2q¹²⁹ + 2q¹³⁰ - 3q¹³¹ + q¹³²

7 q^-105 - 3q^-104 + q^-103 + 5q^-102 - 3q^-101 - 3q^-100 - 6q^-99 + 6q^-98 + 13q^-97 - 9q^-96 + 4q^-95 + 11q^-94 - 14q^-93 - 24q^-92 - 44q^-91 + 2q^-90 + 79q^-89 + 42q^-88 + 66q^-87 + 53q^-86 - 58q^-85 - 136q^-84 - 303q^-83 - 217q^-82 + 100q^-81 + 272q^-80 + 543q^-79 + 613q^-78 + 288q^-77 - 148q^-76 - 1057q^-75 - 1558q^-74 - 1139q^-73 - 408q^-72 + 1160q^-71 + 2534q^-70 + 2964q^-69 + 2515q^-68 - 76q^-67 - 3300q^-66 - 5363q^-65 - 6056q^-64 - 3321q^-63 + 1590q^-62 + 6630q^-61 + 10928q^-60 + 9997q^-59 + 4131q^-58 - 4414q^-57 - 14068q^-56 - 18150q^-55 - 14943q^-54 - 5012q^-53 + 11049q^-52 + 24031q^-51 + 28615q^-50 + 22238q^-49 + 2480q^-48 - 20332q^-47 - 38176q^-46 - 43758q^-45 - 28341q^-44 + 509q^-43 + 34151q^-42 + 60134q^-41 + 60738q^-40 + 36694q^-39 - 6993q^-38 - 57023q^-37 - 86621q^-36 - 85074q^-35 - 45828q^-34 + 23020q^-33 + 88156q^-32 + 126652q^-31 + 115234q^-30 + 47088q^-29 - 48441q^-28 - 139635q^-27 - 181886q^-26 - 143161q^-25 - 38052q^-24 + 102698q^-23 + 217545q^-22 + 242973q^-21 + 163929q^-20 - 6279q^-19 - 198092q^-18 - 315951q^-17 - 304628q^-16 - 143171q^-15 + 108730q^-14 + 332780q^-13 + 428409q^-12 + 323627q^-11 + 47079q^-10 - 275515q^-9 - 503040q^-8 - 502497q^-7 - 250530q^-6 + 142400q^-5 + 507064q^-4 + 646911q^-3 + 471075q^-2 + 51925q^-1 - 433424 - 732689q - 677366q² - 280904q³ + 292499q⁴ + 748498q⁵ + 842248q⁶ + 515423q⁷ - 103849q⁸ - 698377q⁹ - 952809q¹⁰ - 729095q¹¹ - 105025q¹² + 596843q¹³ + 1005049q¹⁴ + 904681q¹⁵ + 311737q¹⁶ - 464207q¹⁷ - 1008835q¹⁸ - 1035467q¹⁹ - 496172q²⁰ + 321900q²¹ + 976647q²² + 1122377q²³ + 649301q²⁴ - 186111q²⁵ - 925729q²⁶ - 1174366q²⁷ - 767224q²⁸ + 69530q²⁹ + 869761q³⁰ + 1201354q³¹ + 853711q³² + 23538q³³ - 820069q³⁴ - 1215920q³⁵ - 916086q³⁶ - 92845q³⁷ + 783101q³⁸ + 1227969q³⁹ + 964206q⁴⁰ + 144221q⁴¹ - 759780q⁴² - 1245203q⁴³ - 1009452q⁴⁴ - 187597q⁴⁵ + 746410q⁴⁶ + 1271349q⁴⁷ + 1061215q⁴⁸ + 234885q⁴⁹ - 732784q⁵⁰ - 1303303q⁵¹ - 1126300q⁵² - 299606q⁵³ + 705063q⁵⁴ + 1332481q⁵⁵ + 1204370q⁵⁶ + 390980q⁵⁷ - 647125q⁵⁸ - 1342653q⁵⁹ - 1286708q⁶⁰ - 512090q⁶¹ + 545256q⁶² + 1314536q⁶³ + 1356333q⁶⁴ + 655093q⁶⁵ - 393982q⁶⁶ - 1230508q⁶⁷ - 1389807q⁶⁸ - 800665q⁶⁹ + 199484q⁷⁰ + 1080639q⁷¹ + 1364500q⁷² + 922380q⁷³ + 18068q⁷⁴ - 869673q⁷⁵ - 1266294q⁷⁶ - 991741q⁷⁷ - 227763q⁷⁸ + 617173q⁷⁹ + 1095124q⁸⁰ + 988808q⁸¹ + 397541q⁸² - 355415q⁸³ - 869481q⁸⁴ - 909006q⁸⁵ - 500862q⁸⁶ + 120754q⁸⁷ + 619520q⁸⁸ + 764882q⁸⁹ + 527985q⁹⁰ + 58293q⁹¹ - 381608q⁹² - 584376q⁹³ - 486164q⁹⁴ - 166238q⁹⁵ + 185801q⁹⁶ + 399254q⁹⁷ + 396985q⁹⁸ + 206381q⁹⁹ - 48084q¹⁰⁰ - 238228q¹⁰¹ - 289047q¹⁰² - 194866q¹⁰³ - 29815q¹⁰⁴ + 117900q¹⁰⁵ + 186189q¹⁰⁶ + 154271q¹⁰⁷ + 60425q¹⁰⁸ - 41237q¹⁰⁹ - 105078q¹¹⁰ - 105985q¹¹¹ - 60331q¹¹² + 1733q¹¹³ + 50372q¹¹⁴ + 63451q¹¹⁵ + 46263q¹¹⁶ + 13087q¹¹⁷ - 19039q¹¹⁸ - 33273q¹¹⁹ - 29965q¹²⁰ - 14385q¹²¹ + 4513q¹²² + 15085q¹²³ + 16707q¹²⁴ + 10672q¹²⁵ + 802q¹²⁶ - 5724q¹²⁷ - 8380q¹²⁸ - 6640q¹²⁹ - 1680q¹³⁰ + 1861q¹³¹ + 3848q¹³² + 3515q¹³³ + 1184q¹³⁴ - 340q¹³⁵ - 1601q¹³⁶ - 1865q¹³⁷ - 757q¹³⁸ + 45q¹³⁹ + 813q¹⁴⁰ + 909q¹⁴¹ + 235q¹⁴² + 56q¹⁴³ - 260q¹⁴⁴ - 470q¹⁴⁵ - 199q¹⁴⁶ - 70q¹⁴⁷ + 221q¹⁴⁸ + 269q¹⁴⁹ - 4q¹⁵⁰ + 17q¹⁵¹ - 34q¹⁵² - 105q¹⁵³ - 36q¹⁵⁴ - 48q¹⁵⁵ + 52q¹⁵⁶ + 81q¹⁵⁷ - 22q¹⁵⁸ + q¹⁵⁹ - 5q¹⁶⁰ - 15q¹⁶¹ + 5q¹⁶² - 18q¹⁶³ + 8q¹⁶⁴ + 19q¹⁶⁵ - 10q¹⁶⁶ - q¹⁶⁷ - 2q¹⁶⁹ + 4q¹⁷⁰ - 4q¹⁷¹ + 2q¹⁷² + 2q¹⁷³ - 3q¹⁷⁴ + q¹⁷⁵

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, 94]]

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

In[3]:=
GaussCode[Knot[10, 94]]

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

In[4]:=
DTCode[Knot[10, 94]]

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

In[5]:=
br = BR[Knot[10, 94]]

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

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

Out[6]=
{3, 10}

In[7]:=
BraidIndex[Knot[10, 94]]

Out[7]=
3

In[8]:=
Show[DrawMorseLink[Knot[10, 94]]]

Out[8]=
-Graphics-

In[9]:=
#[Knot[10, 94]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}

Out[9]=
{Chiral, 2, 4, 3, NotAvailable, 1}

In[10]:=
alex = Alexander[Knot[10, 94]][t]

Out[10]=
-4 4 9 14 2 3 4 -15 - t + -- - -- + -- + 14 t - 9 t + 4 t - t 3 2 t t t

In[11]:=
Conway[Knot[10, 94]][z]

Out[11]=
2 4 6 8 1 - 2 z - 5 z - 4 z - z

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

Out[12]=
{Knot[10, 94]}

In[13]:=
{KnotDet[Knot[10, 94]], KnotSignature[Knot[10, 94]]}

Out[13]=
{71, 2}

In[14]:=
Jones[Knot[10, 94]][q]

Out[14]=
-3 3 6 2 3 4 5 6 7 -8 + q - -- + - + 11 q - 12 q + 11 q - 9 q + 6 q - 3 q + q 2 q q

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

Out[15]=
{Knot[10, 41], Knot[10, 94]}

In[16]:=
A2Invariant[Knot[10, 94]][q]

Out[16]=
-8 -6 2 2 4 6 8 10 14 16 18 20 1 + q - q + -- + 2 q - 3 q + 2 q - 3 q + q - q + 2 q - q + q 4 q

In[17]:=
HOMFLYPT[Knot[10, 94]][a, z]

Out[17]=
2 2 4 4 6 6 8 2 4 2 5 z 12 z 4 4 z 13 z 6 z 6 z z 3 + -- - -- + 5 z + ---- - ----- + 4 z + ---- - ----- + z + -- - ---- - -- 4 2 4 2 4 2 4 2 2 a a a a a a a a a

In[18]:=
Kauffman[Knot[10, 94]][a, z]

Out[18]=
2 2 2 2 2 4 3 z 5 z 3 z 2 z 2 z 6 z 18 z 3 + -- + -- - --- - --- - --- - a z - 7 z - -- + ---- - ---- - ----- + 4 2 5 3 a 8 6 4 2 a a a a a a a a 3 3 3 3 4 4 2 2 3 z 9 z 16 z 10 z 3 4 z 6 z > 2 a z - ---- + ---- + ----- + ----- + 6 a z + 11 z + -- - ---- + 7 5 3 a 8 6 a a a a a 4 4 5 5 5 5 10 z 31 z 2 4 3 z 10 z 15 z 11 z 5 6 > ----- + ----- - 3 a z + ---- - ----- - ----- - ----- - 9 a z - 12 z + 4 2 7 5 3 a a a a a a 6 6 6 7 7 8 8 5 z 9 z 27 z 2 6 6 z 3 z 7 8 5 z 9 z > ---- - ---- - ----- + a z + ---- + ---- + 3 a z + 4 z + ---- + ---- + 6 4 2 5 3 4 2 a a a a a a a 9 9 2 z 2 z > ---- + ---- 3 a a

In[19]:=
{Vassiliev[2][Knot[10, 94]], Vassiliev[3][Knot[10, 94]]}

Out[19]=
{-2, -2}

In[20]:=
Kh[Knot[10, 94]][q, t]

Out[20]=
3 1 2 1 4 2 4 4 q 3 7 q + 5 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 6 q t + 7 4 5 3 3 3 3 2 2 q t t q t q t q t q t q t 5 5 2 7 2 7 3 9 3 9 4 11 4 > 6 q t + 5 q t + 6 q t + 4 q t + 5 q t + 2 q t + 4 q t + 11 5 13 5 15 6 > q t + 2 q t + q t

In[21]:=
ColouredJones[Knot[10, 94], 2][q]

Out[21]=
-10 3 -8 10 15 6 36 27 31 70 2 -24 + q - -- + q + -- - -- - -- + -- - -- - -- + -- - 67 q + 94 q - 9 7 6 5 4 3 2 q q q q q q q q 3 4 5 6 7 8 9 10 11 > 9 q - 97 q + 98 q + 11 q - 104 q + 79 q + 23 q - 81 q + 46 q + 12 13 14 15 16 17 18 19 20 > 20 q - 43 q + 19 q + 9 q - 15 q + 6 q + 2 q - 3 q + q

Dror Bar-Natan: The Knot Atlas: The Rolfsen Knot Table: The Knot 10₉₄

10₉₃
10₉₅

n	Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2	q^-10 - 3q^-9 + q^-8 + 10q^-7 - 15q^-6 - 6q^-5 + 36q^-4 - 27q^-3 - 31q^-2 + 70q^-1 - 24 - 67q + 94q² - 9q³ - 97q⁴ + 98q⁵ + 11q⁶ - 104q⁷ + 79q⁸ + 23q⁹ - 81q¹⁰ + 46q¹¹ + 20q¹² - 43q¹³ + 19q¹⁴ + 9q¹⁵ - 15q¹⁶ + 6q¹⁷ + 2q¹⁸ - 3q¹⁹ + q²⁰
3	q^-21 - 3q^-20 + q^-19 + 5q^-18 + 2q^-17 - 15q^-16 - 8q^-15 + 29q^-14 + 26q^-13 - 44q^-12 - 58q^-11 + 46q^-10 + 112q^-9 - 37q^-8 - 164q^-7 - 9q^-6 + 219q^-5 + 71q^-4 - 245q^-3 - 161q^-2 + 259q^-1 + 241 - 229q - 332q² + 197q³ + 395q⁴ - 137q⁵ - 456q⁶ + 81q⁷ + 492q⁸ - 18q⁹ - 509q¹⁰ - 46q¹¹ + 504q¹² + 102q¹³ - 469q¹⁴ - 148q¹⁵ + 406q¹⁶ + 176q¹⁷ - 321q¹⁸ - 182q¹⁹ + 231q²⁰ + 161q²¹ - 146q²² - 124q²³ + 81q²⁴ + 83q²⁵ - 43q²⁶ - 44q²⁷ + 21q²⁸ + 21q²⁹ - 14q³⁰ - 8q³¹ + 10q³² + 3q³³ - 7q³⁴ + 2q³⁶ + 2q³⁷ - 3q³⁸ + q³⁹
4	q^-36 - 3q^-35 + q^-34 + 5q^-33 - 3q^-32 + 2q^-31 - 18q^-30 + 4q^-29 + 32q^-28 + 2q^-27 + 9q^-26 - 88q^-25 - 34q^-24 + 93q^-23 + 80q^-22 + 113q^-21 - 214q^-20 - 228q^-19 + 34q^-18 + 194q^-17 + 492q^-16 - 152q^-15 - 501q^-14 - 361q^-13 - 5q^-12 + 990q^-11 + 348q^-10 - 383q^-9 - 871q^-8 - 782q^-7 + 1052q^-6 + 996q^-5 + 396q^-4 - 906q^-3 - 1778q^-2 + 412q^-1 + 1195 + 1471q - 259q² - 2417q³ - 568q⁴ + 793q⁵ + 2313q⁶ + 703q⁷ - 2550q⁸ - 1436q⁹ + 122q¹⁰ + 2781q¹¹ + 1582q¹² - 2381q¹³ - 2063q¹⁴ - 546q¹⁵ + 2954q¹⁶ + 2280q¹⁷ - 1987q¹⁸ - 2456q¹⁹ - 1206q²⁰ + 2758q²¹ + 2752q²² - 1261q²³ - 2418q²⁴ - 1809q²⁵ + 2000q²⁶ + 2750q²⁷ - 294q²⁸ - 1745q²⁹ - 2018q³⁰ + 874q³¹ + 2063q³² + 403q³³ - 698q³⁴ - 1566q³⁵ + 5q³⁶ + 1020q³⁷ + 473q³⁸ + 58q³⁹ - 786q⁴⁰ - 231q⁴¹ + 271q⁴² + 187q⁴³ + 235q⁴⁴ - 240q⁴⁵ - 112q⁴⁶ + 20q⁴⁷ - 7q⁴⁸ + 128q⁴⁹ - 49q⁵⁰ - 11q⁵¹ - 34q⁵³ + 39q⁵⁴ - 13q⁵⁵ + 5q⁵⁶ + 5q⁵⁷ - 13q⁵⁸ + 8q⁵⁹ - 4q⁶⁰ + 2q⁶¹ + 2q⁶² - 3q⁶³ + q⁶⁴
5	q^-55 - 3q^-54 + q^-53 + 5q^-52 - 3q^-51 - 3q^-50 - q^-49 - 6q^-48 + 6q^-47 + 27q^-46 + 6q^-45 - 29q^-44 - 39q^-43 - 41q^-42 + 19q^-41 + 113q^-40 + 130q^-39 - 174q^-37 - 277q^-36 - 169q^-35 + 186q^-34 + 511q^-33 + 478q^-32 - 13q^-31 - 678q^-30 - 957q^-29 - 467q^-28 + 592q^-27 + 1450q^-26 + 1298q^-25 - 65q^-24 - 1680q^-23 - 2232q^-22 - 1079q^-21 + 1266q^-20 + 3054q^-19 + 2604q^-18 - 73q^-17 - 3107q^-16 - 4181q^-15 - 2006q^-14 + 2223q^-13 + 5228q^-12 + 4425q^-11 - 84q^-10 - 5237q^-9 - 6808q^-8 - 2899q^-7 + 3926q^-6 + 8388q^-5 + 6417q^-4 - 1349q^-3 - 8940q^-2 - 9668q^-1 - 2169 + 8112q + 12432q² + 6090q³ - 6338q⁴ - 14137q⁵ - 9920q⁶ + 3680q⁷ + 15054q⁸ + 13335q⁹ - 886q¹⁰ - 15114q¹¹ - 16079q¹² - 1980q¹³ + 14765q¹⁴ + 18273q¹⁵ + 4472q¹⁶ - 14173q¹⁷ - 19936q¹⁸ - 6687q¹⁹ + 13516q²⁰ + 21309q²¹ + 8650q²² - 12816q²³ - 22459q²⁴ - 10514q²⁵ + 11921q²⁶ + 23334q²⁷ + 12469q²⁸ - 10608q²⁹ - 23833q³⁰ - 14466q³¹ + 8658q³² + 23618q³³ + 16382q³⁴ - 5971q³⁵ - 22400q³⁶ - 17892q³⁷ + 2694q³⁸ + 20004q³⁹ + 18567q⁴⁰ + 767q⁴¹ - 16463q⁴² - 18039q⁴³ - 3926q⁴⁴ + 12173q⁴⁵ + 16249q⁴⁶ + 6177q⁴⁷ - 7751q⁴⁸ - 13343q⁴⁹ - 7210q⁵⁰ + 3793q⁵¹ + 9896q⁵² + 7029q⁵³ - 867q⁵⁴ - 6507q⁵⁵ - 5879q⁵⁶ - 885q⁵⁷ + 3639q⁵⁸ + 4340q⁵⁹ + 1585q⁶⁰ - 1659q⁶¹ - 2787q⁶² - 1545q⁶³ + 467q⁶⁴ + 1559q⁶⁵ + 1191q⁶⁶ + 68q⁶⁷ - 753q⁶⁸ - 761q⁶⁹ - 218q⁷⁰ + 296q⁷¹ + 416q⁷² + 201q⁷³ - 76q⁷⁴ - 211q⁷⁵ - 136q⁷⁶ + 20q⁷⁷ + 81q⁷⁸ + 61q⁷⁹ + 22q⁸⁰ - 32q⁸¹ - 44q⁸² + 4q⁸³ + 12q⁸⁴ + 11q⁸⁶ - 11q⁸⁸ + 2q⁸⁹ + 4q⁹⁰ - 4q⁹¹ + 2q⁹² + 2q⁹³ - 3q⁹⁴ + q⁹⁵
6	q^-78 - 3q^-77 + q^-76 + 5q^-75 - 3q^-74 - 3q^-73 - 6q^-72 + 11q^-71 - 4q^-70 + q^-69 + 30q^-68 - 13q^-67 - 29q^-66 - 53q^-65 + 17q^-64 + 11q^-63 + 48q^-62 + 162q^-61 + 39q^-60 - 87q^-59 - 289q^-58 - 171q^-57 - 161q^-56 + 97q^-55 + 640q^-54 + 611q^-53 + 333q^-52 - 519q^-51 - 828q^-50 - 1343q^-49 - 917q^-48 + 722q^-47 + 1874q^-46 + 2474q^-45 + 1170q^-44 - 200q^-43 - 3105q^-42 - 4416q^-41 - 2675q^-40 + 490q^-39 + 4516q^-38 + 5829q^-37 + 5846q^-36 + 108q^-35 - 6138q^-34 - 9283q^-33 - 8158q^-32 - 1610q^-31 + 5761q^-30 + 14222q^-29 + 12409q^-28 + 4280q^-27 - 7232q^-26 - 16746q^-25 - 18002q^-24 - 10706q^-23 + 8596q^-22 + 21136q^-21 + 25233q^-20 + 15116q^-19 - 5167q^-18 - 26171q^-17 - 36810q^-16 - 20968q^-15 + 3772q^-14 + 32694q^-13 + 45216q^-12 + 33095q^-11 - 2967q^-10 - 44217q^-9 - 56203q^-8 - 41627q^-7 + 4740q^-6 + 52409q^-5 + 74828q^-4 + 48522q^-3 - 13942q^-2 - 66082q^-1 - 88427 - 50746q + 21863q² + 90405q³ + 99972q⁴ + 42040q⁵ - 40252q⁶ - 109818q⁷ - 105278q⁸ - 31451q⁹ + 73582q¹⁰ + 128048q¹¹ + 96351q¹² + 4767q¹³ - 102946q¹⁴ - 138997q¹⁵ - 82204q¹⁶ + 40951q¹⁷ + 132174q¹⁸ + 132448q¹⁹ + 46553q²⁰ - 83371q²¹ - 152588q²² - 116998q²³ + 11328q²⁴ + 125991q²⁵ + 151950q²⁶ + 75147q²⁷ - 66087q²⁸ - 157689q²⁹ - 138620q³⁰ - 9091q³¹ + 120705q³² + 165160q³³ + 95387q³⁴ - 53444q³⁵ - 162353q³⁶ - 157073q³⁷ - 27884q³⁸ + 114897q³⁹ + 177797q⁴⁰ + 117935q⁴¹ - 34928q⁴² - 161683q⁴³ - 176214q⁴⁴ - 56446q⁴⁵ + 95214q⁴⁶ + 181507q⁴⁷ + 144507q⁴⁸ + 1003q⁴⁹ - 139743q⁵⁰ - 183941q⁵¹ - 93242q⁵² + 50968q⁵³ + 158071q⁵⁴ + 158531q⁵⁵ + 48286q⁵⁶ - 87818q⁵⁷ - 160243q⁵⁸ - 116553q⁵⁹ - 6168q⁶⁰ + 101857q⁶¹ + 138724q⁶² + 80141q⁶³ - 23708q⁶⁴ - 103483q⁶⁵ - 104637q⁶⁶ - 45260q⁶⁷ + 36364q⁶⁸ + 87674q⁶⁹ + 75854q⁷⁰ + 19312q⁷¹ - 41443q⁷² - 64110q⁷³ - 48249q⁷⁴ - 5452q⁷⁵ + 35069q⁷⁶ + 45846q⁷⁷ + 27437q⁷⁸ - 4001q⁷⁹ - 24253q⁸⁰ - 28684q⁸¹ - 15195q⁸² + 5570q⁸³ + 17335q⁸⁴ + 16309q⁸⁵ + 5863q⁸⁶ - 3749q⁸⁷ - 10398q⁸⁸ - 9329q⁸⁹ - 2211q⁹⁰ + 3575q⁹¹ + 5717q⁹² + 3791q⁹³ + 1253q⁹⁴ - 2206q⁹⁵ - 3400q⁹⁶ - 1663q⁹⁷ + 89q⁹⁸ + 1275q⁹⁹ + 1192q¹⁰⁰ + 1025q¹⁰¹ - 187q¹⁰² - 929q¹⁰³ - 535q¹⁰⁴ - 186q¹⁰⁵ + 191q¹⁰⁶ + 213q¹⁰⁷ + 398q¹⁰⁸ + 49q¹⁰⁹ - 230q¹¹⁰ - 106q¹¹¹ - 67q¹¹² + 24q¹¹³ + 114q¹¹⁵ + 23q¹¹⁶ - 58q¹¹⁷ - 7q¹¹⁸ - 12q¹¹⁹ + 10q¹²⁰ - 16q¹²¹ + 24q¹²² + 6q¹²³ - 16q¹²⁴ + 4q¹²⁵ - 2q¹²⁶ + 4q¹²⁷ - 4q¹²⁸ + 2q¹²⁹ + 2q¹³⁰ - 3q¹³¹ + q¹³²
7	q^-105 - 3q^-104 + q^-103 + 5q^-102 - 3q^-101 - 3q^-100 - 6q^-99 + 6q^-98 + 13q^-97 - 9q^-96 + 4q^-95 + 11q^-94 - 14q^-93 - 24q^-92 - 44q^-91 + 2q^-90 + 79q^-89 + 42q^-88 + 66q^-87 + 53q^-86 - 58q^-85 - 136q^-84 - 303q^-83 - 217q^-82 + 100q^-81 + 272q^-80 + 543q^-79 + 613q^-78 + 288q^-77 - 148q^-76 - 1057q^-75 - 1558q^-74 - 1139q^-73 - 408q^-72 + 1160q^-71 + 2534q^-70 + 2964q^-69 + 2515q^-68 - 76q^-67 - 3300q^-66 - 5363q^-65 - 6056q^-64 - 3321q^-63 + 1590q^-62 + 6630q^-61 + 10928q^-60 + 9997q^-59 + 4131q^-58 - 4414q^-57 - 14068q^-56 - 18150q^-55 - 14943q^-54 - 5012q^-53 + 11049q^-52 + 24031q^-51 + 28615q^-50 + 22238q^-49 + 2480q^-48 - 20332q^-47 - 38176q^-46 - 43758q^-45 - 28341q^-44 + 509q^-43 + 34151q^-42 + 60134q^-41 + 60738q^-40 + 36694q^-39 - 6993q^-38 - 57023q^-37 - 86621q^-36 - 85074q^-35 - 45828q^-34 + 23020q^-33 + 88156q^-32 + 126652q^-31 + 115234q^-30 + 47088q^-29 - 48441q^-28 - 139635q^-27 - 181886q^-26 - 143161q^-25 - 38052q^-24 + 102698q^-23 + 217545q^-22 + 242973q^-21 + 163929q^-20 - 6279q^-19 - 198092q^-18 - 315951q^-17 - 304628q^-16 - 143171q^-15 + 108730q^-14 + 332780q^-13 + 428409q^-12 + 323627q^-11 + 47079q^-10 - 275515q^-9 - 503040q^-8 - 502497q^-7 - 250530q^-6 + 142400q^-5 + 507064q^-4 + 646911q^-3 + 471075q^-2 + 51925q^-1 - 433424 - 732689q - 677366q² - 280904q³ + 292499q⁴ + 748498q⁵ + 842248q⁶ + 515423q⁷ - 103849q⁸ - 698377q⁹ - 952809q¹⁰ - 729095q¹¹ - 105025q¹² + 596843q¹³ + 1005049q¹⁴ + 904681q¹⁵ + 311737q¹⁶ - 464207q¹⁷ - 1008835q¹⁸ - 1035467q¹⁹ - 496172q²⁰ + 321900q²¹ + 976647q²² + 1122377q²³ + 649301q²⁴ - 186111q²⁵ - 925729q²⁶ - 1174366q²⁷ - 767224q²⁸ + 69530q²⁹ + 869761q³⁰ + 1201354q³¹ + 853711q³² + 23538q³³ - 820069q³⁴ - 1215920q³⁵ - 916086q³⁶ - 92845q³⁷ + 783101q³⁸ + 1227969q³⁹ + 964206q⁴⁰ + 144221q⁴¹ - 759780q⁴² - 1245203q⁴³ - 1009452q⁴⁴ - 187597q⁴⁵ + 746410q⁴⁶ + 1271349q⁴⁷ + 1061215q⁴⁸ + 234885q⁴⁹ - 732784q⁵⁰ - 1303303q⁵¹ - 1126300q⁵² - 299606q⁵³ + 705063q⁵⁴ + 1332481q⁵⁵ + 1204370q⁵⁶ + 390980q⁵⁷ - 647125q⁵⁸ - 1342653q⁵⁹ - 1286708q⁶⁰ - 512090q⁶¹ + 545256q⁶² + 1314536q⁶³ + 1356333q⁶⁴ + 655093q⁶⁵ - 393982q⁶⁶ - 1230508q⁶⁷ - 1389807q⁶⁸ - 800665q⁶⁹ + 199484q⁷⁰ + 1080639q⁷¹ + 1364500q⁷² + 922380q⁷³ + 18068q⁷⁴ - 869673q⁷⁵ - 1266294q⁷⁶ - 991741q⁷⁷ - 227763q⁷⁸ + 617173q⁷⁹ + 1095124q⁸⁰ + 988808q⁸¹ + 397541q⁸² - 355415q⁸³ - 869481q⁸⁴ - 909006q⁸⁵ - 500862q⁸⁶ + 120754q⁸⁷ + 619520q⁸⁸ + 764882q⁸⁹ + 527985q⁹⁰ + 58293q⁹¹ - 381608q⁹² - 584376q⁹³ - 486164q⁹⁴ - 166238q⁹⁵ + 185801q⁹⁶ + 399254q⁹⁷ + 396985q⁹⁸ + 206381q⁹⁹ - 48084q¹⁰⁰ - 238228q¹⁰¹ - 289047q¹⁰² - 194866q¹⁰³ - 29815q¹⁰⁴ + 117900q¹⁰⁵ + 186189q¹⁰⁶ + 154271q¹⁰⁷ + 60425q¹⁰⁸ - 41237q¹⁰⁹ - 105078q¹¹⁰ - 105985q¹¹¹ - 60331q¹¹² + 1733q¹¹³ + 50372q¹¹⁴ + 63451q¹¹⁵ + 46263q¹¹⁶ + 13087q¹¹⁷ - 19039q¹¹⁸ - 33273q¹¹⁹ - 29965q¹²⁰ - 14385q¹²¹ + 4513q¹²² + 15085q¹²³ + 16707q¹²⁴ + 10672q¹²⁵ + 802q¹²⁶ - 5724q¹²⁷ - 8380q¹²⁸ - 6640q¹²⁹ - 1680q¹³⁰ + 1861q¹³¹ + 3848q¹³² + 3515q¹³³ + 1184q¹³⁴ - 340q¹³⁵ - 1601q¹³⁶ - 1865q¹³⁷ - 757q¹³⁸ + 45q¹³⁹ + 813q¹⁴⁰ + 909q¹⁴¹ + 235q¹⁴² + 56q¹⁴³ - 260q¹⁴⁴ - 470q¹⁴⁵ - 199q¹⁴⁶ - 70q¹⁴⁷ + 221q¹⁴⁸ + 269q¹⁴⁹ - 4q¹⁵⁰ + 17q¹⁵¹ - 34q¹⁵² - 105q¹⁵³ - 36q¹⁵⁴ - 48q¹⁵⁵ + 52q¹⁵⁶ + 81q¹⁵⁷ - 22q¹⁵⁸ + q¹⁵⁹ - 5q¹⁶⁰ - 15q¹⁶¹ + 5q¹⁶² - 18q¹⁶³ + 8q¹⁶⁴ + 19q¹⁶⁵ - 10q¹⁶⁶ - q¹⁶⁷ - 2q¹⁶⁹ + 4q¹⁷⁰ - 4q¹⁷¹ + 2q¹⁷² + 2q¹⁷³ - 3q¹⁷⁴ + q¹⁷⁵

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 30, 2005, 10:15:35)...
In[2]:=	PD[Knot[10, 94]]
Out[2]=	PD[X[6, 2, 7, 1], X[2, 8, 3, 7], X[18, 12, 19, 11], X[14, 5, 15, 6], > X[20, 14, 1, 13], X[8, 15, 9, 16], X[10, 4, 11, 3], X[16, 9, 17, 10], > X[4, 17, 5, 18], X[12, 20, 13, 19]]
In[3]:=	GaussCode[Knot[10, 94]]
Out[3]=	GaussCode[1, -2, 7, -9, 4, -1, 2, -6, 8, -7, 3, -10, 5, -4, 6, -8, 9, -3, 10, > -5]
In[4]:=	DTCode[Knot[10, 94]]
Out[4]=	DTCode[6, 10, 14, 2, 16, 18, 20, 8, 4, 12]
In[5]:=	br = BR[Knot[10, 94]]
Out[5]=	BR[3, {1, 1, 1, -2, 1, 1, -2, -2, 1, -2}]
In[6]:=	{First[br], Crossings[br]}
Out[6]=	{3, 10}
In[7]:=	BraidIndex[Knot[10, 94]]
Out[7]=	3
In[8]:=	Show[DrawMorseLink[Knot[10, 94]]]

Out[8]=	-Graphics-
In[9]:=	#[Knot[10, 94]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}
Out[9]=	{Chiral, 2, 4, 3, NotAvailable, 1}
In[10]:=	alex = Alexander[Knot[10, 94]][t]
Out[10]=	-4 4 9 14 2 3 4 -15 - t + -- - -- + -- + 14 t - 9 t + 4 t - t 3 2 t t t
In[11]:=	Conway[Knot[10, 94]][z]
Out[11]=	2 4 6 8 1 - 2 z - 5 z - 4 z - z
In[12]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]=	{Knot[10, 94]}
In[13]:=	{KnotDet[Knot[10, 94]], KnotSignature[Knot[10, 94]]}
Out[13]=	{71, 2}
In[14]:=	Jones[Knot[10, 94]][q]
Out[14]=	-3 3 6 2 3 4 5 6 7 -8 + q - -- + - + 11 q - 12 q + 11 q - 9 q + 6 q - 3 q + q 2 q q
In[15]:=	Select[AllKnots[], (J === Jones[#][q] \|\| (J /. q-> 1/q) === Jones[#][q])&]
Out[15]=	{Knot[10, 41], Knot[10, 94]}
In[16]:=	A2Invariant[Knot[10, 94]][q]
Out[16]=	-8 -6 2 2 4 6 8 10 14 16 18 20 1 + q - q + -- + 2 q - 3 q + 2 q - 3 q + q - q + 2 q - q + q 4 q
In[17]:=	HOMFLYPT[Knot[10, 94]][a, z]
Out[17]=	2 2 4 4 6 6 8 2 4 2 5 z 12 z 4 4 z 13 z 6 z 6 z z 3 + -- - -- + 5 z + ---- - ----- + 4 z + ---- - ----- + z + -- - ---- - -- 4 2 4 2 4 2 4 2 2 a a a a a a a a a
In[18]:=	Kauffman[Knot[10, 94]][a, z]
Out[18]=	2 2 2 2 2 4 3 z 5 z 3 z 2 z 2 z 6 z 18 z 3 + -- + -- - --- - --- - --- - a z - 7 z - -- + ---- - ---- - ----- + 4 2 5 3 a 8 6 4 2 a a a a a a a a 3 3 3 3 4 4 2 2 3 z 9 z 16 z 10 z 3 4 z 6 z > 2 a z - ---- + ---- + ----- + ----- + 6 a z + 11 z + -- - ---- + 7 5 3 a 8 6 a a a a a 4 4 5 5 5 5 10 z 31 z 2 4 3 z 10 z 15 z 11 z 5 6 > ----- + ----- - 3 a z + ---- - ----- - ----- - ----- - 9 a z - 12 z + 4 2 7 5 3 a a a a a a 6 6 6 7 7 8 8 5 z 9 z 27 z 2 6 6 z 3 z 7 8 5 z 9 z > ---- - ---- - ----- + a z + ---- + ---- + 3 a z + 4 z + ---- + ---- + 6 4 2 5 3 4 2 a a a a a a a 9 9 2 z 2 z > ---- + ---- 3 a a
In[19]:=	{Vassiliev[2][Knot[10, 94]], Vassiliev[3][Knot[10, 94]]}
Out[19]=	{-2, -2}
In[20]:=	Kh[Knot[10, 94]][q, t]
Out[20]=	3 1 2 1 4 2 4 4 q 3 7 q + 5 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 6 q t + 7 4 5 3 3 3 3 2 2 q t t q t q t q t q t q t 5 5 2 7 2 7 3 9 3 9 4 11 4 > 6 q t + 5 q t + 6 q t + 4 q t + 5 q t + 2 q t + 4 q t + 11 5 13 5 15 6 > q t + 2 q t + q t
In[21]:=	ColouredJones[Knot[10, 94], 2][q]
Out[21]=	-10 3 -8 10 15 6 36 27 31 70 2 -24 + q - -- + q + -- - -- - -- + -- - -- - -- + -- - 67 q + 94 q - 9 7 6 5 4 3 2 q q q q q q q q 3 4 5 6 7 8 9 10 11 > 9 q - 97 q + 98 q + 11 q - 104 q + 79 q + 23 q - 81 q + 46 q + 12 13 14 15 16 17 18 19 20 > 20 q - 43 q + 19 q + 9 q - 15 q + 6 q + 2 q - 3 q + q

The Alternating Knot 1094

The Alternating Knot 10₉₄