The Alternating Knot 9₁₁

Visit 9₁₁'s page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 9₁₁'s page at Knotilus!

Acknowledgement

KnotPlot

PD Presentation: X₁₄₂₅ X_9,12,10,13 X_3,11,4,10 X_11,3,12,2 X_13,1,14,18 X_5,15,6,14 X_7,17,8,16 X_15,7,16,6 X_17,9,18,8

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

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

Minimum Braid Representative:

Length is 9, width is 4
Braid index is 4

A Morse Link Presentation:

3D Invariants:

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

Reversible 2 3 2 / 4--6 1

Alexander Polynomial: - t^-3 + 5t^-2 - 7t^-1 + 7 - 7t + 5t² - t³

Conway Polynomial: 1 + 4z² - z⁴ - z⁶

Other knots with the same Alexander/Conway Polynomial: {K11n95, ...}

Determinant and Signature: {33, 4}

Jones Polynomial: 1 - 2q + 3q² - 4q³ + 6q⁴ - 5q⁵ + 5q⁶ - 4q⁷ + 2q⁸ - q⁹

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

A2 (sl(3)) Invariant: 1 - q⁸ + 2q¹⁰ + 2q¹⁴ + q¹⁶ + q²⁰ - q²² - q²⁶ - q²⁸

HOMFLY-PT Polynomial: - 2a^-8 - a^-8z² + 3a^-6 + 6a^-6z² + 2a^-6z⁴ - a^-4 - 4a^-4z² - 4a^-4z⁴ - a^-4z⁶ + a^-2 + 3a^-2z² + a^-2z⁴

Kauffman Polynomial: - a^-11z + a^-11z³ - a^-10z² + 2a^-10z⁴ + 2a^-9z - 3a^-9z³ + 3a^-9z⁵ - 2a^-8 + 4a^-8z² - 4a^-8z⁴ + 3a^-8z⁶ + 2a^-7z - 3a^-7z³ - a^-7z⁵ + 2a^-7z⁷ - 3a^-6 + 6a^-6z² - 7a^-6z⁴ + a^-6z⁶ + a^-6z⁸ - 2a^-5z + 9a^-5z³ - 12a^-5z⁵ + 4a^-5z⁷ - a^-4 + 5a^-4z² - 5a^-4z⁴ - a^-4z⁶ + a^-4z⁸ - a^-3z + 8a^-3z³ - 8a^-3z⁵ + 2a^-3z⁷ - a^-2 + 4a^-2z² - 4a^-2z⁴ + a^-2z⁶

V₂ and V₃, the type 2 and 3 Vassiliev invariants: {4, 9}

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=4 is the signature of 9₁₁. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.)

t^rq^j r = -2 r = -1 r = 0 r = 1 r = 2 r = 3 r = 4 r = 5 r = 6 r = 7

j = 19 1

j = 17 1

j = 15 3 1

j = 13 2 1

j = 11 3 3

j = 9 3 2

j = 7 1 3

j = 5 2 3

j = 3 1 2

j = 1 1

j = -1 1

n Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2 q^-2 - 2q^-1 - 1 + 6q - 4q² - 6q³ + 13q⁴ - 3q⁵ - 14q⁶ + 18q⁷ - 22q⁹ + 21q¹⁰ + 5q¹¹ - 26q¹² + 19q¹³ + 9q¹⁴ - 25q¹⁵ + 14q¹⁶ + 7q¹⁷ - 17q¹⁸ + 9q¹⁹ + 3q²⁰ - 8q²¹ + 4q²² + q²³ - 2q²⁴ + q²⁵

3 q^-6 - 2q^-5 - q^-4 + 2q^-3 + 5q^-2 - 3q^-1 - 9 + q + 15q² + 2q³ - 18q⁴ - 10q⁵ + 22q⁶ + 17q⁷ - 21q⁸ - 25q⁹ + 19q¹⁰ + 31q¹¹ - 12q¹² - 37q¹³ + 9q¹⁴ + 37q¹⁵ + q¹⁶ - 43q¹⁷ - 3q¹⁸ + 37q¹⁹ + 17q²⁰ - 43q²¹ - 18q²² + 35q²³ + 30q²⁴ - 37q²⁵ - 28q²⁶ + 27q²⁷ + 32q²⁸ - 25q²⁹ - 26q³⁰ + 18q³¹ + 19q³² - 13q³³ - 14q³⁴ + 13q³⁵ + 5q³⁶ - 8q³⁷ - 4q³⁸ + 9q³⁹ - 5q⁴¹ - q⁴² + 5q⁴³ - q⁴⁴ - q⁴⁵ - q⁴⁶ + 2q⁴⁷ - q⁴⁸

4 q^-12 - 2q^-11 - q^-10 + 2q^-9 + q^-8 + 6q^-7 - 7q^-6 - 7q^-5 + q^-3 + 25q^-2 - 6q^-1 - 17 - 13q - 13q² + 49q³ + 10q⁴ - 10q⁵ - 27q⁶ - 51q⁷ + 57q⁸ + 27q⁹ + 19q¹⁰ - 19q¹¹ - 89q¹² + 41q¹³ + 17q¹⁴ + 50q¹⁵ + 16q¹⁶ - 103q¹⁷ + 23q¹⁸ - 22q¹⁹ + 58q²⁰ + 58q²¹ - 87q²² + 23q²³ - 72q²⁴ + 41q²⁵ + 89q²⁶ - 58q²⁷ + 36q²⁸ - 117q²⁹ + 14q³⁰ + 112q³¹ - 25q³² + 46q³³ - 154q³⁴ - 11q³⁵ + 128q³⁶ + 10q³⁷ + 56q³⁸ - 180q³⁹ - 39q⁴⁰ + 126q⁴¹ + 43q⁴² + 72q⁴³ - 178q⁴⁴ - 62q⁴⁵ + 96q⁴⁶ + 47q⁴⁷ + 91q⁴⁸ - 134q⁴⁹ - 65q⁵⁰ + 50q⁵¹ + 21q⁵² + 90q⁵³ - 74q⁵⁴ - 40q⁵⁵ + 17q⁵⁶ - 11q⁵⁷ + 63q⁵⁸ - 30q⁵⁹ - 11q⁶⁰ + 6q⁶¹ - 23q⁶² + 32q⁶³ - 11q⁶⁴ + 3q⁶⁵ + 4q⁶⁶ - 17q⁶⁷ + 13q⁶⁸ - 5q⁶⁹ + 3q⁷⁰ + 3q⁷¹ - 7q⁷² + 4q⁷³ - 2q⁷⁴ + q⁷⁵ + q⁷⁶ - 2q⁷⁷ + q⁷⁸

5 q^-20 - 2q^-19 - q^-18 + 2q^-17 + q^-16 + 2q^-15 + 2q^-14 - 5q^-13 - 9q^-12 + 5q^-10 + 10q^-9 + 14q^-8 - 2q^-7 - 22q^-6 - 23q^-5 - 5q^-4 + 18q^-3 + 39q^-2 + 28q^-1 - 16 - 48q - 48q² - 8q³ + 49q⁴ + 70q⁵ + 36q⁶ - 32q⁷ - 80q⁸ - 70q⁹ + 7q¹⁰ + 73q¹¹ + 86q¹² + 35q¹³ - 47q¹⁴ - 95q¹⁵ - 61q¹⁶ + 9q¹⁷ + 70q¹⁸ + 81q¹⁹ + 37q²⁰ - 36q²¹ - 69q²² - 73q²³ - 23q²⁴ + 46q²⁵ + 88q²⁶ + 79q²⁷ + 15q²⁸ - 94q²⁹ - 141q³⁰ - 67q³¹ + 69q³² + 174q³³ + 157q³⁴ - 36q³⁵ - 224q³⁶ - 207q³⁷ - 9q³⁸ + 222q³⁹ + 294q⁴⁰ + 59q⁴¹ - 261q⁴² - 328q⁴³ - 98q⁴⁴ + 240q⁴⁵ + 400q⁴⁶ + 146q⁴⁷ - 279q⁴⁸ - 425q⁴⁹ - 172q⁵⁰ + 257q⁵¹ + 489q⁵² + 216q⁵³ - 296q⁵⁴ - 512q⁵⁵ - 242q⁵⁶ + 270q⁵⁷ + 568q⁵⁸ + 287q⁵⁹ - 284q⁶⁰ - 568q⁶¹ - 325q⁶² + 232q⁶³ + 584q⁶⁴ + 366q⁶⁵ - 198q⁶⁶ - 545q⁶⁷ - 384q⁶⁸ + 121q⁶⁹ + 492q⁷⁰ + 392q⁷¹ - 58q⁷² - 414q⁷³ - 367q⁷⁴ + 6q⁷⁵ + 314q⁷⁶ + 320q⁷⁷ + 45q⁷⁸ - 232q⁷⁹ - 263q⁸⁰ - 52q⁸¹ + 145q⁸² + 190q⁸³ + 71q⁸⁴ - 92q⁸⁵ - 135q⁸⁶ - 51q⁸⁷ + 40q⁸⁸ + 85q⁸⁹ + 49q⁹⁰ - 22q⁹¹ - 50q⁹² - 28q⁹³ - q⁹⁴ + 27q⁹⁵ + 27q⁹⁶ - 4q⁹⁷ - 13q⁹⁸ - 8q⁹⁹ - 7q¹⁰⁰ + 4q¹⁰¹ + 13q¹⁰² - 3q¹⁰³ - 3q¹⁰⁴ + 2q¹⁰⁵ - 4q¹⁰⁶ - q¹⁰⁷ + 5q¹⁰⁸ - 2q¹⁰⁹ - q¹¹⁰ + 2q¹¹¹ - q¹¹² - q¹¹³ + 2q¹¹⁴ - q¹¹⁵

6 q^-30 - 2q^-29 - q^-28 + 2q^-27 + q^-26 + 2q^-25 - 2q^-24 + 4q^-23 - 7q^-22 - 9q^-21 + 3q^-20 + 4q^-19 + 11q^-18 + 2q^-17 + 19q^-16 - 14q^-15 - 29q^-14 - 15q^-13 - 8q^-12 + 19q^-11 + 13q^-10 + 71q^-9 + 8q^-8 - 38q^-7 - 49q^-6 - 58q^-5 - 19q^-4 - 13q^-3 + 135q^-2 + 78q^-1 + 25 - 36q - 94q² - 103q³ - 133q⁴ + 121q⁵ + 110q⁶ + 129q⁷ + 67q⁸ - 15q⁹ - 113q¹⁰ - 266q¹¹ + 12q¹² + 5q¹³ + 124q¹⁴ + 133q¹⁵ + 150q¹⁶ + 32q¹⁷ - 240q¹⁸ - 24q¹⁹ - 155q²⁰ - 42q²¹ - 8q²² + 193q²³ + 198q²⁴ - 44q²⁵ + 171q²⁶ - 138q²⁷ - 196q²⁸ - 318q²⁹ - 21q³⁰ + 149q³¹ + 117q³² + 522q³³ + 159q³⁴ - 118q³⁵ - 572q³⁶ - 384q³⁷ - 180q³⁸ + 36q³⁹ + 804q⁴⁰ + 607q⁴¹ + 226q⁴² - 594q⁴³ - 685q⁴⁴ - 644q⁴⁵ - 291q⁴⁶ + 865q⁴⁷ + 1007q⁴⁸ + 697q⁴⁹ - 391q⁵⁰ - 805q⁵¹ - 1067q⁵² - 726q⁵³ + 729q⁵⁴ + 1257q⁵⁵ + 1136q⁵⁶ - 91q⁵⁷ - 775q⁵⁸ - 1363q⁵⁹ - 1124q⁶⁰ + 513q⁶¹ + 1388q⁶² + 1469q⁶³ + 179q⁶⁴ - 707q⁶⁵ - 1568q⁶⁶ - 1415q⁶⁷ + 337q⁶⁸ + 1490q⁶⁹ + 1717q⁷⁰ + 371q⁷¹ - 687q⁷² - 1755q⁷³ - 1630q⁷⁴ + 225q⁷⁵ + 1608q⁷⁶ + 1940q⁷⁷ + 546q⁷⁸ - 684q⁷⁹ - 1932q⁸⁰ - 1842q⁸¹ + 73q⁸² + 1654q⁸³ + 2129q⁸⁴ + 788q⁸⁵ - 553q⁸⁶ - 1968q⁸⁷ - 2027q⁸⁸ - 213q⁸⁹ + 1460q⁹⁰ + 2132q⁹¹ + 1046q⁹² - 220q⁹³ - 1700q⁹⁴ - 2011q⁹⁵ - 535q⁹⁶ + 1003q⁹⁷ + 1803q⁹⁸ + 1111q⁹⁹ + 161q¹⁰⁰ - 1161q¹⁰¹ - 1664q¹⁰² - 661q¹⁰³ + 488q¹⁰⁴ + 1227q¹⁰⁵ + 881q¹⁰⁶ + 354q¹⁰⁷ - 601q¹⁰⁸ - 1111q¹⁰⁹ - 524q¹¹⁰ + 152q¹¹¹ + 664q¹¹² + 511q¹¹³ + 323q¹¹⁴ - 232q¹¹⁵ - 608q¹¹⁶ - 292q¹¹⁷ + 20q¹¹⁸ + 297q¹¹⁹ + 215q¹²⁰ + 209q¹²¹ - 64q¹²² - 291q¹²³ - 120q¹²⁴ - 12q¹²⁵ + 116q¹²⁶ + 63q¹²⁷ + 116q¹²⁸ - 6q¹²⁹ - 130q¹³⁰ - 37q¹³¹ - 14q¹³² + 40q¹³³ + 7q¹³⁴ + 58q¹³⁵ + 7q¹³⁶ - 54q¹³⁷ - 5q¹³⁸ - 8q¹³⁹ + 12q¹⁴⁰ - 7q¹⁴¹ + 24q¹⁴² + 5q¹⁴³ - 20q¹⁴⁴ + 4q¹⁴⁵ - 3q¹⁴⁶ + 4q¹⁴⁷ - 6q¹⁴⁸ + 7q¹⁴⁹ + 2q¹⁵⁰ - 7q¹⁵¹ + 4q¹⁵² - q¹⁵³ + q¹⁵⁴ - 2q¹⁵⁵ + q¹⁵⁶ + q¹⁵⁷ - 2q¹⁵⁸ + q¹⁵⁹

7 q^-42 - 2q^-41 - q^-40 + 2q^-39 + q^-38 + 2q^-37 - 2q^-36 + 2q^-34 - 7q^-33 - 6q^-32 + 2q^-31 + 4q^-30 + 13q^-29 + 4q^-28 + 10q^-26 - 18q^-25 - 25q^-24 - 18q^-23 - 10q^-22 + 29q^-21 + 28q^-20 + 26q^-19 + 48q^-18 - 5q^-17 - 43q^-16 - 63q^-15 - 91q^-14 - 9q^-13 + 27q^-12 + 56q^-11 + 140q^-10 + 86q^-9 + 30q^-8 - 54q^-7 - 188q^-6 - 140q^-5 - 96q^-4 - 32q^-3 + 171q^-2 + 194q^-1 + 207 + 145q - 124q² - 185q³ - 257q⁴ - 268q⁵ - 10q⁶ + 93q⁷ + 259q⁸ + 370q⁹ + 132q¹⁰ + 45q¹¹ - 148q¹² - 365q¹³ - 208q¹⁴ - 215q¹⁵ - 33q¹⁶ + 251q¹⁷ + 179q¹⁸ + 308q¹⁹ + 226q²⁰ - 43q²¹ + 4q²² - 254q²³ - 356q²⁴ - 204q²⁵ - 307q²⁶ + 48q²⁷ + 327q²⁸ + 353q²⁹ + 661q³⁰ + 347q³¹ - 83q³² - 378q³³ - 963q³⁴ - 807q³⁵ - 345q³⁶ + 143q³⁷ + 1114q³⁸ + 1275q³⁹ + 913q⁴⁰ + 302q⁴¹ - 1031q⁴² - 1615q⁴³ - 1537q⁴⁴ - 940q⁴⁵ + 727q⁴⁶ + 1755q⁴⁷ + 2072q⁴⁸ + 1671q⁴⁹ - 152q⁵⁰ - 1659q⁵¹ - 2499q⁵² - 2433q⁵³ - 519q⁵⁴ + 1345q⁵⁵ + 2678q⁵⁶ + 3083q⁵⁷ + 1334q⁵⁸ - 801q⁵⁹ - 2703q⁶⁰ - 3659q⁶¹ - 2103q⁶² + 193q⁶³ + 2500q⁶⁴ + 4003q⁶⁵ + 2853q⁶⁶ + 559q⁶⁷ - 2176q⁶⁸ - 4289q⁶⁹ - 3499q⁷⁰ - 1225q⁷¹ + 1766q⁷² + 4347q⁷³ + 4033q⁷⁴ + 1945q⁷⁵ - 1303q⁷⁶ - 4406q⁷⁷ - 4495q⁷⁸ - 2499q⁷⁹ + 887q⁸⁰ + 4332q⁸¹ + 4820q⁸² + 3046q⁸³ - 473q⁸⁴ - 4318q⁸⁵ - 5137q⁸⁶ - 3430q⁸⁷ + 198q⁸⁸ + 4260q⁸⁹ + 5348q⁹⁰ + 3797q⁹¹ + 62q⁹² - 4306q⁹³ - 5621q⁹⁴ - 4049q⁹⁵ - 184q⁹⁶ + 4336q⁹⁷ + 5844q⁹⁸ + 4346q⁹⁹ + 335q¹⁰⁰ - 4461q¹⁰¹ - 6136q¹⁰² - 4589q¹⁰³ - 469q¹⁰⁴ + 4489q¹⁰⁵ + 6390q¹⁰⁶ + 4953q¹⁰⁷ + 705q¹⁰⁸ - 4495q¹⁰⁹ - 6611q¹¹⁰ - 5271q¹¹¹ - 1042q¹¹² + 4265q¹¹³ + 6687q¹¹⁴ + 5635q¹¹⁵ + 1516q¹¹⁶ - 3889q¹¹⁷ - 6578q¹¹⁸ - 5841q¹¹⁹ - 2021q¹²⁰ + 3261q¹²¹ + 6162q¹²² + 5901q¹²³ + 2526q¹²⁴ - 2501q¹²⁵ - 5533q¹²⁶ - 5677q¹²⁷ - 2859q¹²⁸ + 1697q¹²⁹ + 4652q¹³⁰ + 5166q¹³¹ + 3000q¹³² - 935q¹³³ - 3683q¹³⁴ - 4463q¹³⁵ - 2886q¹³⁶ + 379q¹³⁷ + 2730q¹³⁸ + 3585q¹³⁹ + 2534q¹⁴⁰ + 23q¹⁴¹ - 1871q¹⁴² - 2729q¹⁴³ - 2093q¹⁴⁴ - 185q¹⁴⁵ + 1239q¹⁴⁶ + 1928q¹⁴⁷ + 1559q¹⁴⁸ + 222q¹⁴⁹ - 738q¹⁵⁰ - 1304q¹⁵¹ - 1113q¹⁵² - 162q¹⁵³ + 451q¹⁵⁴ + 830q¹⁵⁵ + 726q¹⁵⁶ + 94q¹⁵⁷ - 270q¹⁵⁸ - 521q¹⁵⁹ - 454q¹⁶⁰ - 16q¹⁶¹ + 161q¹⁶² + 307q¹⁶³ + 291q¹⁶⁴ - 16q¹⁶⁵ - 109q¹⁶⁶ - 205q¹⁶⁷ - 172q¹⁶⁸ + 49q¹⁶⁹ + 64q¹⁷⁰ + 113q¹⁷¹ + 115q¹⁷² - 29q¹⁷³ - 39q¹⁷⁴ - 89q¹⁷⁵ - 80q¹⁷⁶ + 43q¹⁷⁷ + 26q¹⁷⁸ + 38q¹⁷⁹ + 48q¹⁸⁰ - 16q¹⁸¹ - q¹⁸² - 38q¹⁸³ - 40q¹⁸⁴ + 24q¹⁸⁵ + 6q¹⁸⁶ + 9q¹⁸⁷ + 18q¹⁸⁸ - 7q¹⁸⁹ + 7q¹⁹⁰ - 12q¹⁹¹ - 17q¹⁹² + 13q¹⁹³ - 2q¹⁹⁴ + q¹⁹⁵ + 5q¹⁹⁶ - 4q¹⁹⁷ + 5q¹⁹⁸ - 3q¹⁹⁹ - 5q²⁰⁰ + 6q²⁰¹ - 2q²⁰² - q²⁰³ + q²⁰⁴ - q²⁰⁵ + 2q²⁰⁶ - q²⁰⁷ - q²⁰⁸ + 2q²⁰⁹ - q²¹⁰

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[9, 11]]

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

In[3]:=
GaussCode[Knot[9, 11]]

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

In[4]:=
DTCode[Knot[9, 11]]

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

In[5]:=
br = BR[Knot[9, 11]]

Out[5]=
BR[4, {1, 1, 1, 1, -2, 1, 3, -2, 3}]

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

Out[6]=
{4, 9}

In[7]:=
BraidIndex[Knot[9, 11]]

Out[7]=
4

In[8]:=
Show[DrawMorseLink[Knot[9, 11]]]

Out[8]=
-Graphics-

In[9]:=
#[Knot[9, 11]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}

Out[9]=
{Reversible, 2, 3, 2, {4, 6}, 1}

In[10]:=
alex = Alexander[Knot[9, 11]][t]

Out[10]=
-3 5 7 2 3 7 - t + -- - - - 7 t + 5 t - t 2 t t

In[11]:=
Conway[Knot[9, 11]][z]

Out[11]=
2 4 6 1 + 4 z - z - z

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

Out[12]=
{Knot[9, 11], Knot[11, NonAlternating, 95]}

In[13]:=
{KnotDet[Knot[9, 11]], KnotSignature[Knot[9, 11]]}

Out[13]=
{33, 4}

In[14]:=
Jones[Knot[9, 11]][q]

Out[14]=
2 3 4 5 6 7 8 9 1 - 2 q + 3 q - 4 q + 6 q - 5 q + 5 q - 4 q + 2 q - q

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

Out[15]=
{Knot[9, 11]}

In[16]:=
A2Invariant[Knot[9, 11]][q]

Out[16]=
8 10 14 16 20 22 26 28 1 - q + 2 q + 2 q + q + q - q - q - q

In[17]:=
HOMFLYPT[Knot[9, 11]][a, z]

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

In[18]:=
Kauffman[Knot[9, 11]][a, z]

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

In[19]:=
{Vassiliev[2][Knot[9, 11]], Vassiliev[3][Knot[9, 11]]}

Out[19]=
{4, 9}

In[20]:=
Kh[Knot[9, 11]][q, t]

Out[20]=
3 3 5 1 q q 5 7 7 2 9 2 9 3 2 q + 2 q + ---- + - + -- + 3 q t + q t + 3 q t + 3 q t + 2 q t + 2 t t q t 11 3 11 4 13 4 13 5 15 5 15 6 17 6 > 3 q t + 3 q t + 2 q t + q t + 3 q t + q t + q t + 19 7 > q t

In[21]:=
ColouredJones[Knot[9, 11], 2][q]

Out[21]=
-2 2 2 3 4 5 6 7 9 -1 + q - - + 6 q - 4 q - 6 q + 13 q - 3 q - 14 q + 18 q - 22 q + q 10 11 12 13 14 15 16 17 > 21 q + 5 q - 26 q + 19 q + 9 q - 25 q + 14 q + 7 q - 18 19 20 21 22 23 24 25 > 17 q + 9 q + 3 q - 8 q + 4 q + q - 2 q + q

Dror Bar-Natan: The Knot Atlas: The Rolfsen Knot Table: The Knot 9₁₁

9₁₀
9₁₂

n	Coloured Jones Polynomial (in the (n+1)-dimensional representation of sl(2))
2	q^-2 - 2q^-1 - 1 + 6q - 4q² - 6q³ + 13q⁴ - 3q⁵ - 14q⁶ + 18q⁷ - 22q⁹ + 21q¹⁰ + 5q¹¹ - 26q¹² + 19q¹³ + 9q¹⁴ - 25q¹⁵ + 14q¹⁶ + 7q¹⁷ - 17q¹⁸ + 9q¹⁹ + 3q²⁰ - 8q²¹ + 4q²² + q²³ - 2q²⁴ + q²⁵
3	q^-6 - 2q^-5 - q^-4 + 2q^-3 + 5q^-2 - 3q^-1 - 9 + q + 15q² + 2q³ - 18q⁴ - 10q⁵ + 22q⁶ + 17q⁷ - 21q⁸ - 25q⁹ + 19q¹⁰ + 31q¹¹ - 12q¹² - 37q¹³ + 9q¹⁴ + 37q¹⁵ + q¹⁶ - 43q¹⁷ - 3q¹⁸ + 37q¹⁹ + 17q²⁰ - 43q²¹ - 18q²² + 35q²³ + 30q²⁴ - 37q²⁵ - 28q²⁶ + 27q²⁷ + 32q²⁸ - 25q²⁹ - 26q³⁰ + 18q³¹ + 19q³² - 13q³³ - 14q³⁴ + 13q³⁵ + 5q³⁶ - 8q³⁷ - 4q³⁸ + 9q³⁹ - 5q⁴¹ - q⁴² + 5q⁴³ - q⁴⁴ - q⁴⁵ - q⁴⁶ + 2q⁴⁷ - q⁴⁸
4	q^-12 - 2q^-11 - q^-10 + 2q^-9 + q^-8 + 6q^-7 - 7q^-6 - 7q^-5 + q^-3 + 25q^-2 - 6q^-1 - 17 - 13q - 13q² + 49q³ + 10q⁴ - 10q⁵ - 27q⁶ - 51q⁷ + 57q⁸ + 27q⁹ + 19q¹⁰ - 19q¹¹ - 89q¹² + 41q¹³ + 17q¹⁴ + 50q¹⁵ + 16q¹⁶ - 103q¹⁷ + 23q¹⁸ - 22q¹⁹ + 58q²⁰ + 58q²¹ - 87q²² + 23q²³ - 72q²⁴ + 41q²⁵ + 89q²⁶ - 58q²⁷ + 36q²⁸ - 117q²⁹ + 14q³⁰ + 112q³¹ - 25q³² + 46q³³ - 154q³⁴ - 11q³⁵ + 128q³⁶ + 10q³⁷ + 56q³⁸ - 180q³⁹ - 39q⁴⁰ + 126q⁴¹ + 43q⁴² + 72q⁴³ - 178q⁴⁴ - 62q⁴⁵ + 96q⁴⁶ + 47q⁴⁷ + 91q⁴⁸ - 134q⁴⁹ - 65q⁵⁰ + 50q⁵¹ + 21q⁵² + 90q⁵³ - 74q⁵⁴ - 40q⁵⁵ + 17q⁵⁶ - 11q⁵⁷ + 63q⁵⁸ - 30q⁵⁹ - 11q⁶⁰ + 6q⁶¹ - 23q⁶² + 32q⁶³ - 11q⁶⁴ + 3q⁶⁵ + 4q⁶⁶ - 17q⁶⁷ + 13q⁶⁸ - 5q⁶⁹ + 3q⁷⁰ + 3q⁷¹ - 7q⁷² + 4q⁷³ - 2q⁷⁴ + q⁷⁵ + q⁷⁶ - 2q⁷⁷ + q⁷⁸
5	q^-20 - 2q^-19 - q^-18 + 2q^-17 + q^-16 + 2q^-15 + 2q^-14 - 5q^-13 - 9q^-12 + 5q^-10 + 10q^-9 + 14q^-8 - 2q^-7 - 22q^-6 - 23q^-5 - 5q^-4 + 18q^-3 + 39q^-2 + 28q^-1 - 16 - 48q - 48q² - 8q³ + 49q⁴ + 70q⁵ + 36q⁶ - 32q⁷ - 80q⁸ - 70q⁹ + 7q¹⁰ + 73q¹¹ + 86q¹² + 35q¹³ - 47q¹⁴ - 95q¹⁵ - 61q¹⁶ + 9q¹⁷ + 70q¹⁸ + 81q¹⁹ + 37q²⁰ - 36q²¹ - 69q²² - 73q²³ - 23q²⁴ + 46q²⁵ + 88q²⁶ + 79q²⁷ + 15q²⁸ - 94q²⁹ - 141q³⁰ - 67q³¹ + 69q³² + 174q³³ + 157q³⁴ - 36q³⁵ - 224q³⁶ - 207q³⁷ - 9q³⁸ + 222q³⁹ + 294q⁴⁰ + 59q⁴¹ - 261q⁴² - 328q⁴³ - 98q⁴⁴ + 240q⁴⁵ + 400q⁴⁶ + 146q⁴⁷ - 279q⁴⁸ - 425q⁴⁹ - 172q⁵⁰ + 257q⁵¹ + 489q⁵² + 216q⁵³ - 296q⁵⁴ - 512q⁵⁵ - 242q⁵⁶ + 270q⁵⁷ + 568q⁵⁸ + 287q⁵⁹ - 284q⁶⁰ - 568q⁶¹ - 325q⁶² + 232q⁶³ + 584q⁶⁴ + 366q⁶⁵ - 198q⁶⁶ - 545q⁶⁷ - 384q⁶⁸ + 121q⁶⁹ + 492q⁷⁰ + 392q⁷¹ - 58q⁷² - 414q⁷³ - 367q⁷⁴ + 6q⁷⁵ + 314q⁷⁶ + 320q⁷⁷ + 45q⁷⁸ - 232q⁷⁹ - 263q⁸⁰ - 52q⁸¹ + 145q⁸² + 190q⁸³ + 71q⁸⁴ - 92q⁸⁵ - 135q⁸⁶ - 51q⁸⁷ + 40q⁸⁸ + 85q⁸⁹ + 49q⁹⁰ - 22q⁹¹ - 50q⁹² - 28q⁹³ - q⁹⁴ + 27q⁹⁵ + 27q⁹⁶ - 4q⁹⁷ - 13q⁹⁸ - 8q⁹⁹ - 7q¹⁰⁰ + 4q¹⁰¹ + 13q¹⁰² - 3q¹⁰³ - 3q¹⁰⁴ + 2q¹⁰⁵ - 4q¹⁰⁶ - q¹⁰⁷ + 5q¹⁰⁸ - 2q¹⁰⁹ - q¹¹⁰ + 2q¹¹¹ - q¹¹² - q¹¹³ + 2q¹¹⁴ - q¹¹⁵
6	q^-30 - 2q^-29 - q^-28 + 2q^-27 + q^-26 + 2q^-25 - 2q^-24 + 4q^-23 - 7q^-22 - 9q^-21 + 3q^-20 + 4q^-19 + 11q^-18 + 2q^-17 + 19q^-16 - 14q^-15 - 29q^-14 - 15q^-13 - 8q^-12 + 19q^-11 + 13q^-10 + 71q^-9 + 8q^-8 - 38q^-7 - 49q^-6 - 58q^-5 - 19q^-4 - 13q^-3 + 135q^-2 + 78q^-1 + 25 - 36q - 94q² - 103q³ - 133q⁴ + 121q⁵ + 110q⁶ + 129q⁷ + 67q⁸ - 15q⁹ - 113q¹⁰ - 266q¹¹ + 12q¹² + 5q¹³ + 124q¹⁴ + 133q¹⁵ + 150q¹⁶ + 32q¹⁷ - 240q¹⁸ - 24q¹⁹ - 155q²⁰ - 42q²¹ - 8q²² + 193q²³ + 198q²⁴ - 44q²⁵ + 171q²⁶ - 138q²⁷ - 196q²⁸ - 318q²⁹ - 21q³⁰ + 149q³¹ + 117q³² + 522q³³ + 159q³⁴ - 118q³⁵ - 572q³⁶ - 384q³⁷ - 180q³⁸ + 36q³⁹ + 804q⁴⁰ + 607q⁴¹ + 226q⁴² - 594q⁴³ - 685q⁴⁴ - 644q⁴⁵ - 291q⁴⁶ + 865q⁴⁷ + 1007q⁴⁸ + 697q⁴⁹ - 391q⁵⁰ - 805q⁵¹ - 1067q⁵² - 726q⁵³ + 729q⁵⁴ + 1257q⁵⁵ + 1136q⁵⁶ - 91q⁵⁷ - 775q⁵⁸ - 1363q⁵⁹ - 1124q⁶⁰ + 513q⁶¹ + 1388q⁶² + 1469q⁶³ + 179q⁶⁴ - 707q⁶⁵ - 1568q⁶⁶ - 1415q⁶⁷ + 337q⁶⁸ + 1490q⁶⁹ + 1717q⁷⁰ + 371q⁷¹ - 687q⁷² - 1755q⁷³ - 1630q⁷⁴ + 225q⁷⁵ + 1608q⁷⁶ + 1940q⁷⁷ + 546q⁷⁸ - 684q⁷⁹ - 1932q⁸⁰ - 1842q⁸¹ + 73q⁸² + 1654q⁸³ + 2129q⁸⁴ + 788q⁸⁵ - 553q⁸⁶ - 1968q⁸⁷ - 2027q⁸⁸ - 213q⁸⁹ + 1460q⁹⁰ + 2132q⁹¹ + 1046q⁹² - 220q⁹³ - 1700q⁹⁴ - 2011q⁹⁵ - 535q⁹⁶ + 1003q⁹⁷ + 1803q⁹⁸ + 1111q⁹⁹ + 161q¹⁰⁰ - 1161q¹⁰¹ - 1664q¹⁰² - 661q¹⁰³ + 488q¹⁰⁴ + 1227q¹⁰⁵ + 881q¹⁰⁶ + 354q¹⁰⁷ - 601q¹⁰⁸ - 1111q¹⁰⁹ - 524q¹¹⁰ + 152q¹¹¹ + 664q¹¹² + 511q¹¹³ + 323q¹¹⁴ - 232q¹¹⁵ - 608q¹¹⁶ - 292q¹¹⁷ + 20q¹¹⁸ + 297q¹¹⁹ + 215q¹²⁰ + 209q¹²¹ - 64q¹²² - 291q¹²³ - 120q¹²⁴ - 12q¹²⁵ + 116q¹²⁶ + 63q¹²⁷ + 116q¹²⁸ - 6q¹²⁹ - 130q¹³⁰ - 37q¹³¹ - 14q¹³² + 40q¹³³ + 7q¹³⁴ + 58q¹³⁵ + 7q¹³⁶ - 54q¹³⁷ - 5q¹³⁸ - 8q¹³⁹ + 12q¹⁴⁰ - 7q¹⁴¹ + 24q¹⁴² + 5q¹⁴³ - 20q¹⁴⁴ + 4q¹⁴⁵ - 3q¹⁴⁶ + 4q¹⁴⁷ - 6q¹⁴⁸ + 7q¹⁴⁹ + 2q¹⁵⁰ - 7q¹⁵¹ + 4q¹⁵² - q¹⁵³ + q¹⁵⁴ - 2q¹⁵⁵ + q¹⁵⁶ + q¹⁵⁷ - 2q¹⁵⁸ + q¹⁵⁹
7	q^-42 - 2q^-41 - q^-40 + 2q^-39 + q^-38 + 2q^-37 - 2q^-36 + 2q^-34 - 7q^-33 - 6q^-32 + 2q^-31 + 4q^-30 + 13q^-29 + 4q^-28 + 10q^-26 - 18q^-25 - 25q^-24 - 18q^-23 - 10q^-22 + 29q^-21 + 28q^-20 + 26q^-19 + 48q^-18 - 5q^-17 - 43q^-16 - 63q^-15 - 91q^-14 - 9q^-13 + 27q^-12 + 56q^-11 + 140q^-10 + 86q^-9 + 30q^-8 - 54q^-7 - 188q^-6 - 140q^-5 - 96q^-4 - 32q^-3 + 171q^-2 + 194q^-1 + 207 + 145q - 124q² - 185q³ - 257q⁴ - 268q⁵ - 10q⁶ + 93q⁷ + 259q⁸ + 370q⁹ + 132q¹⁰ + 45q¹¹ - 148q¹² - 365q¹³ - 208q¹⁴ - 215q¹⁵ - 33q¹⁶ + 251q¹⁷ + 179q¹⁸ + 308q¹⁹ + 226q²⁰ - 43q²¹ + 4q²² - 254q²³ - 356q²⁴ - 204q²⁵ - 307q²⁶ + 48q²⁷ + 327q²⁸ + 353q²⁹ + 661q³⁰ + 347q³¹ - 83q³² - 378q³³ - 963q³⁴ - 807q³⁵ - 345q³⁶ + 143q³⁷ + 1114q³⁸ + 1275q³⁹ + 913q⁴⁰ + 302q⁴¹ - 1031q⁴² - 1615q⁴³ - 1537q⁴⁴ - 940q⁴⁵ + 727q⁴⁶ + 1755q⁴⁷ + 2072q⁴⁸ + 1671q⁴⁹ - 152q⁵⁰ - 1659q⁵¹ - 2499q⁵² - 2433q⁵³ - 519q⁵⁴ + 1345q⁵⁵ + 2678q⁵⁶ + 3083q⁵⁷ + 1334q⁵⁸ - 801q⁵⁹ - 2703q⁶⁰ - 3659q⁶¹ - 2103q⁶² + 193q⁶³ + 2500q⁶⁴ + 4003q⁶⁵ + 2853q⁶⁶ + 559q⁶⁷ - 2176q⁶⁸ - 4289q⁶⁹ - 3499q⁷⁰ - 1225q⁷¹ + 1766q⁷² + 4347q⁷³ + 4033q⁷⁴ + 1945q⁷⁵ - 1303q⁷⁶ - 4406q⁷⁷ - 4495q⁷⁸ - 2499q⁷⁹ + 887q⁸⁰ + 4332q⁸¹ + 4820q⁸² + 3046q⁸³ - 473q⁸⁴ - 4318q⁸⁵ - 5137q⁸⁶ - 3430q⁸⁷ + 198q⁸⁸ + 4260q⁸⁹ + 5348q⁹⁰ + 3797q⁹¹ + 62q⁹² - 4306q⁹³ - 5621q⁹⁴ - 4049q⁹⁵ - 184q⁹⁶ + 4336q⁹⁷ + 5844q⁹⁸ + 4346q⁹⁹ + 335q¹⁰⁰ - 4461q¹⁰¹ - 6136q¹⁰² - 4589q¹⁰³ - 469q¹⁰⁴ + 4489q¹⁰⁵ + 6390q¹⁰⁶ + 4953q¹⁰⁷ + 705q¹⁰⁸ - 4495q¹⁰⁹ - 6611q¹¹⁰ - 5271q¹¹¹ - 1042q¹¹² + 4265q¹¹³ + 6687q¹¹⁴ + 5635q¹¹⁵ + 1516q¹¹⁶ - 3889q¹¹⁷ - 6578q¹¹⁸ - 5841q¹¹⁹ - 2021q¹²⁰ + 3261q¹²¹ + 6162q¹²² + 5901q¹²³ + 2526q¹²⁴ - 2501q¹²⁵ - 5533q¹²⁶ - 5677q¹²⁷ - 2859q¹²⁸ + 1697q¹²⁹ + 4652q¹³⁰ + 5166q¹³¹ + 3000q¹³² - 935q¹³³ - 3683q¹³⁴ - 4463q¹³⁵ - 2886q¹³⁶ + 379q¹³⁷ + 2730q¹³⁸ + 3585q¹³⁹ + 2534q¹⁴⁰ + 23q¹⁴¹ - 1871q¹⁴² - 2729q¹⁴³ - 2093q¹⁴⁴ - 185q¹⁴⁵ + 1239q¹⁴⁶ + 1928q¹⁴⁷ + 1559q¹⁴⁸ + 222q¹⁴⁹ - 738q¹⁵⁰ - 1304q¹⁵¹ - 1113q¹⁵² - 162q¹⁵³ + 451q¹⁵⁴ + 830q¹⁵⁵ + 726q¹⁵⁶ + 94q¹⁵⁷ - 270q¹⁵⁸ - 521q¹⁵⁹ - 454q¹⁶⁰ - 16q¹⁶¹ + 161q¹⁶² + 307q¹⁶³ + 291q¹⁶⁴ - 16q¹⁶⁵ - 109q¹⁶⁶ - 205q¹⁶⁷ - 172q¹⁶⁸ + 49q¹⁶⁹ + 64q¹⁷⁰ + 113q¹⁷¹ + 115q¹⁷² - 29q¹⁷³ - 39q¹⁷⁴ - 89q¹⁷⁵ - 80q¹⁷⁶ + 43q¹⁷⁷ + 26q¹⁷⁸ + 38q¹⁷⁹ + 48q¹⁸⁰ - 16q¹⁸¹ - q¹⁸² - 38q¹⁸³ - 40q¹⁸⁴ + 24q¹⁸⁵ + 6q¹⁸⁶ + 9q¹⁸⁷ + 18q¹⁸⁸ - 7q¹⁸⁹ + 7q¹⁹⁰ - 12q¹⁹¹ - 17q¹⁹² + 13q¹⁹³ - 2q¹⁹⁴ + q¹⁹⁵ + 5q¹⁹⁶ - 4q¹⁹⁷ + 5q¹⁹⁸ - 3q¹⁹⁹ - 5q²⁰⁰ + 6q²⁰¹ - 2q²⁰² - q²⁰³ + q²⁰⁴ - q²⁰⁵ + 2q²⁰⁶ - q²⁰⁷ - q²⁰⁸ + 2q²⁰⁹ - q²¹⁰

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

Out[8]=	-Graphics-
In[9]:=	#[Knot[9, 11]]& /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}
Out[9]=	{Reversible, 2, 3, 2, {4, 6}, 1}
In[10]:=	alex = Alexander[Knot[9, 11]][t]
Out[10]=	-3 5 7 2 3 7 - t + -- - - - 7 t + 5 t - t 2 t t
In[11]:=	Conway[Knot[9, 11]][z]
Out[11]=	2 4 6 1 + 4 z - z - z
In[12]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]=	{Knot[9, 11], Knot[11, NonAlternating, 95]}
In[13]:=	{KnotDet[Knot[9, 11]], KnotSignature[Knot[9, 11]]}
Out[13]=	{33, 4}
In[14]:=	Jones[Knot[9, 11]][q]
Out[14]=	2 3 4 5 6 7 8 9 1 - 2 q + 3 q - 4 q + 6 q - 5 q + 5 q - 4 q + 2 q - q
In[15]:=	Select[AllKnots[], (J === Jones[#][q] \|\| (J /. q-> 1/q) === Jones[#][q])&]
Out[15]=	{Knot[9, 11]}
In[16]:=	A2Invariant[Knot[9, 11]][q]
Out[16]=	8 10 14 16 20 22 26 28 1 - q + 2 q + 2 q + q + q - q - q - q
In[17]:=	HOMFLYPT[Knot[9, 11]][a, z]
Out[17]=	2 2 2 2 4 4 4 6 -2 3 -4 -2 z 6 z 4 z 3 z 2 z 4 z z z -- + -- - a + a - -- + ---- - ---- + ---- + ---- - ---- + -- - -- 8 6 8 6 4 2 6 4 2 4 a a a a a a a a a a
In[18]:=	Kauffman[Knot[9, 11]][a, z]
Out[18]=	2 2 2 2 -2 3 -4 -2 z 2 z 2 z 2 z z z 4 z 6 z 5 z -- - -- - a - a - --- + --- + --- - --- - -- - --- + ---- + ---- + ---- + 8 6 11 9 7 5 3 10 8 6 4 a a a a a a a a a a a 2 3 3 3 3 3 4 4 4 4 4 4 z z 3 z 3 z 9 z 8 z 2 z 4 z 7 z 5 z 4 z > ---- + --- - ---- - ---- + ---- + ---- + ---- - ---- - ---- - ---- - ---- + 2 11 9 7 5 3 10 8 6 4 2 a a a a a a a a a a a 5 5 5 5 6 6 6 6 7 7 7 8 3 z z 12 z 8 z 3 z z z z 2 z 4 z 2 z z > ---- - -- - ----- - ---- + ---- + -- - -- + -- + ---- + ---- + ---- + -- + 9 7 5 3 8 6 4 2 7 5 3 6 a a a a a a a a a a a a 8 z > -- 4 a
In[19]:=	{Vassiliev[2][Knot[9, 11]], Vassiliev[3][Knot[9, 11]]}
Out[19]=	{4, 9}
In[20]:=	Kh[Knot[9, 11]][q, t]
Out[20]=	3 3 5 1 q q 5 7 7 2 9 2 9 3 2 q + 2 q + ---- + - + -- + 3 q t + q t + 3 q t + 3 q t + 2 q t + 2 t t q t 11 3 11 4 13 4 13 5 15 5 15 6 17 6 > 3 q t + 3 q t + 2 q t + q t + 3 q t + q t + q t + 19 7 > q t
In[21]:=	ColouredJones[Knot[9, 11], 2][q]
Out[21]=	-2 2 2 3 4 5 6 7 9 -1 + q - - + 6 q - 4 q - 6 q + 13 q - 3 q - 14 q + 18 q - 22 q + q 10 11 12 13 14 15 16 17 > 21 q + 5 q - 26 q + 19 q + 9 q - 25 q + 14 q + 7 q - 18 19 20 21 22 23 24 25 > 17 q + 9 q + 3 q - 8 q + 4 q + q - 2 q + q

The Alternating Knot 911

The Alternating Knot 9₁₁