# K11n150

## Contents

 (Knotscape image) See the full Hoste-Thistlethwaite Table of 11 Crossing Knots. Visit K11n150's page at Knotilus! Visit K11n150's page at the original Knot Atlas!

### Knot presentations

 Planar diagram presentation X6271 X8394 X10,6,11,5 X18,8,19,7 X16,9,17,10 X11,1,12,22 X13,21,14,20 X4,16,5,15 X2,17,3,18 X19,15,20,14 X21,13,22,12 Gauss code 1, -9, 2, -8, 3, -1, 4, -2, 5, -3, -6, 11, -7, 10, 8, -5, 9, -4, -10, 7, -11, 6 Dowker-Thistlethwaite code 6 8 10 18 16 -22 -20 4 2 -14 -12
A Braid Representative

### Three dimensional invariants

 Symmetry type Reversible Unknotting number {1,2} 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index Missing Maximal Thurston-Bennequin number Data:K11n150/ThurstonBennequinNumber Hyperbolic Volume 14.7873 A-Polynomial See Data:K11n150/A-polynomial

### Four dimensional invariants

 Smooth 4 genus Missing Topological 4 genus Missing Concordance genus 3 Rasmussen s-Invariant -2

### Polynomial invariants

 Alexander polynomial 2t3−9t2 + 17t−19 + 17t−1−9t−2 + 2t−3 Conway polynomial 2z6 + 3z4−z2 + 1 2nd Alexander ideal (db, data sources) {1} Determinant and Signature { 75, 2 } Jones polynomial 2q7−5q6 + 8q5−12q4 + 13q3−12q2 + 11q−7 + 4q−1−q−2 HOMFLY-PT polynomial (db, data sources) z6a−2 + z6a−4 + 2z4a−2 + 3z4a−4−z4a−6−z4 + 3z2a−4−3z2a−6−z2 + a−4−2a−6 + a−8 + 1 Kauffman polynomial (db, data sources) 2z9a−3 + 2z9a−5 + 5z8a−2 + 8z8a−4 + 3z8a−6 + 6z7a−1 + 3z7a−3−2z7a−5 + z7a−7−6z6a−2−17z6a−4−7z6a−6 + 4z6 + az5−10z5a−1−6z5a−3 + 8z5a−5 + 3z5a−7 + 19z4a−4 + 15z4a−6 + 3z4a−8−7z4−az3 + 2z3a−1−2z3a−3−12z3a−5−7z3a−7−z2a−2−10z2a−4−12z2a−6−5z2a−8 + 2z2 + 3za−3 + 7za−5 + 4za−7 + a−4 + 2a−6 + a−8 + 1 The A2 invariant Data:K11n150/QuantumInvariant/A2/1,0 The G2 invariant Data:K11n150/QuantumInvariant/G2/1,0

### "Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11a258,}

Same Jones Polynomial (up to mirroring, $q\leftrightarrow q^{-1}$): {K11n66,}

### Vassiliev invariants

 V2 and V3: (-1, -3)
V2,1 through V6,9:
 V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 −4 −24 8 $-\frac{254}{3}$ $-\frac{58}{3}$ 96 −112 0 −56 $-\frac{32}{3}$ 288 $\frac{1016}{3}$ $\frac{232}{3}$ $\frac{16049}{30}$ $\frac{982}{15}$ $\frac{11578}{45}$ $-\frac{1937}{18}$ $\frac{1649}{30}$

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

### Khovanov Homology

The coefficients of the monomials trqj are shown, along with their alternating sums χ (fixed j, alternation over r). 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 K11n150. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
 \ r \ j \
-3-2-10123456χ
15         22
13        3 -3
11       52 3
9      73  -4
7     65   1
5    67    1
3   56     -1
1  37      4
-1 14       -3
-3 3        3
-51         -1
Integral Khovanov Homology
 $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ i = 1 i = 3 r = −3 ${\mathbb Z}$ r = −2 ${\mathbb Z}^{3}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ r = −1 ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ r = 0 ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{5}$ r = 1 ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{6}$ r = 2 ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{6}$ r = 3 ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ r = 4 ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ r = 5 ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ r = 6 ${\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$

### Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory. See A Sample KnotTheory Session.

Read me first: Modifying Knot Pages.

See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

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