10 146

10_145

10_147

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10 146 Further Notes and Views

Knot presentations

Planar diagram presentation	X4251 X5,18,6,19 X8394 X2,9,3,10 X11,17,12,16 X7,12,8,13 X15,6,16,7 X17,11,18,10 X13,1,14,20 X19,15,20,14
Gauss code	1, -4, 3, -1, -2, 7, -6, -3, 4, 8, -5, 6, -9, 10, -7, 5, -8, 2, -10, 9
Dowker-Thistlethwaite code	4 8 -18 -12 2 -16 -20 -6 -10 -14
Conway Notation	[22,21,21-]

Minimum Braid Representative: Length is 11, width is 4. Braid index is 4.

A Morse Link Presentation:

Three dimensional invariants

Symmetry type Reversible Unknotting number 1 3-genus 2 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-4] Hyperbolic Volume 10.561 A-Polynomial See Data:10 146/A-polynomial

[edit Notes for 10 146's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $2$ Rasmussen s-Invariant 0

[edit Notes for 10 146's four dimensional invariants]

Polynomial invariants

Alexander polynomial	$2t^{2}-8t+13-8t^{-1}+2t^{-2}$
Conway polynomial	$2z^{4}+1$
2nd Alexander ideal (db, data sources)	$\{1\}$
Determinant and Signature	{ 33, 0 }
Jones polynomial	$-q^{3}+3q^{2}-4q+6-6q^{-1}+5q^{-2}-4q^{-3}+3q^{-4}-q^{-5}$
HOMFLY-PT polynomial (db, data sources)	$-z^{2}a^{4}+z^{4}a^{2}+z^{2}a^{2}+z^{4}+z^{2}+1-z^{2}a^{-2}$
Kauffman polynomial (db, data sources)	$a^{2}z^{8}+z^{8}+3a^{3}z^{7}+4az^{7}+z^{7}a^{-1}+3a^{4}z^{6}+a^{2}z^{6}-2z^{6}+a^{5}z^{5}-8a^{3}z^{5}-11az^{5}-2z^{5}a^{-1}-8a^{4}z^{4}-6a^{2}z^{4}+3z^{4}a^{-2}+5z^{4}-2a^{5}z^{3}+5a^{3}z^{3}+12az^{3}+6z^{3}a^{-1}+z^{3}a^{-3}+3a^{4}z^{2}+3a^{2}z^{2}-3z^{2}a^{-2}-3z^{2}-a^{3}z-3az-3za^{-1}-za^{-3}+1$
The A2 invariant	$-q^{16}+q^{14}+q^{12}-q^{10}+q^{8}-q^{6}+q^{2}+2q^{-2}-q^{-4}+q^{-6}+q^{-8}-q^{-10}$
The G2 invariant	$q^{80}-2q^{78}+4q^{76}-7q^{74}+5q^{72}-2q^{70}-6q^{68}+16q^{66}-19q^{64}+20q^{62}-13q^{60}-4q^{58}+19q^{56}-29q^{54}+29q^{52}-14q^{50}-4q^{48}+20q^{46}-22q^{44}+16q^{42}-q^{40}-18q^{38}+23q^{36}-21q^{34}+7q^{32}+13q^{30}-31q^{28}+37q^{26}-24q^{24}+10q^{22}+6q^{20}-27q^{18}+34q^{16}-31q^{14}+22q^{12}-3q^{10}-15q^{8}+28q^{6}-23q^{4}+12q^{2}+4-18q^{-2}+20q^{-4}-13q^{-6}-q^{-8}+22q^{-10}-29q^{-12}+27q^{-14}-11q^{-16}-8q^{-18}+22q^{-20}-27q^{-22}+19q^{-24}-8q^{-26}+q^{-28}+8q^{-30}-12q^{-32}+8q^{-34}-3q^{-36}+2q^{-38}-2q^{-42}-q^{-44}+q^{-48}-q^{-50}+q^{-52}$

Further Quantum Invariants

Further quantum knot invariants for 10_146.

A1 Invariants.

Weight	Invariant
1	$-q^{11}+2q^{9}-q^{7}+q^{5}-q^{3}+2q^{-1}-q^{-3}+2q^{-5}-q^{-7}$
2	$q^{32}-2q^{30}-2q^{28}+6q^{26}-7q^{22}+4q^{20}+4q^{18}-8q^{16}+7q^{12}-3q^{10}-q^{8}+5q^{6}+q^{4}-5q^{2}-1+7q^{-2}-5q^{-4}-5q^{-6}+9q^{-8}-5q^{-12}+4q^{-14}+q^{-16}-2q^{-18}$
3	$-q^{63}+2q^{61}+2q^{59}-3q^{57}-6q^{55}+13q^{51}+5q^{49}-13q^{47}-14q^{45}+8q^{43}+23q^{41}-28q^{37}-13q^{35}+25q^{33}+26q^{31}-18q^{29}-32q^{27}+11q^{25}+33q^{23}-2q^{21}-31q^{19}-4q^{17}+25q^{15}+7q^{13}-19q^{11}-11q^{9}+15q^{7}+16q^{5}-4q^{3}-23q-3q^{-1}+27q^{-3}+14q^{-5}-26q^{-7}-26q^{-9}+22q^{-11}+32q^{-13}-12q^{-15}-32q^{-17}+q^{-19}+26q^{-21}+8q^{-23}-17q^{-25}-8q^{-27}+6q^{-29}+8q^{-31}-q^{-33}-4q^{-35}-q^{-37}+q^{-41}$

A2 Invariants.

Weight	Invariant
1,0	$-q^{16}+q^{14}+q^{12}-q^{10}+q^{8}-q^{6}+q^{2}+2q^{-2}-q^{-4}+q^{-6}+q^{-8}-q^{-10}$
1,1	$q^{44}-4q^{42}+10q^{40}-22q^{38}+38q^{36}-54q^{34}+72q^{32}-86q^{30}+85q^{28}-70q^{26}+42q^{24}-4q^{22}-41q^{20}+86q^{18}-122q^{16}+146q^{14}-153q^{12}+146q^{10}-126q^{8}+96q^{6}-52q^{4}+12q^{2}+34-62q^{-2}+80q^{-4}-92q^{-6}+80q^{-8}-64q^{-10}+43q^{-12}-22q^{-14}+14q^{-16}-2q^{-24}-2q^{-26}+q^{-28}$
2,0	$q^{42}-q^{40}-2q^{38}+3q^{34}+3q^{32}-4q^{30}-2q^{28}+2q^{26}+2q^{24}-3q^{22}-4q^{20}+3q^{18}+2q^{16}-q^{14}+4q^{10}+q^{8}+q^{6}+2q^{4}-2q^{2}-1+q^{-4}-5q^{-6}-2q^{-8}+6q^{-10}+3q^{-12}-3q^{-14}+4q^{-18}+2q^{-20}-2q^{-22}-2q^{-24}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{34}-2q^{32}+2q^{28}-4q^{26}+4q^{24}+2q^{22}-5q^{20}+4q^{18}+q^{16}-5q^{14}+q^{12}+2q^{10}-2q^{8}+q^{4}+3q^{2}-q^{-2}+7q^{-4}-3q^{-6}-2q^{-8}+6q^{-10}-3q^{-12}-3q^{-14}+3q^{-16}-q^{-18}-q^{-20}+q^{-22}$
1,0,0	$-q^{21}+q^{19}+q^{15}-q^{13}+q^{11}-q^{9}+q^{3}+q+2q^{-3}-q^{-5}+q^{-7}+q^{-11}-q^{-13}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{44}-q^{42}-2q^{40}+2q^{38}+q^{36}-3q^{34}+5q^{30}-q^{28}-5q^{26}+2q^{24}+6q^{22}-3q^{20}-4q^{18}+6q^{16}-6q^{12}+2q^{8}-4q^{6}-q^{4}+7q^{2}+3-q^{-2}+5q^{-4}+8q^{-6}-3q^{-8}-3q^{-10}+3q^{-12}-5q^{-16}-2q^{-18}+2q^{-20}+q^{-22}-q^{-24}+q^{-28}$
1,0,0,0	$-q^{26}+q^{24}+q^{18}-q^{16}+q^{14}-q^{12}+q^{4}+q^{2}+1+2q^{-4}-q^{-6}+q^{-8}+q^{-14}-q^{-16}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{34}+2q^{32}-4q^{30}+6q^{28}-6q^{26}+6q^{24}-6q^{22}+5q^{20}-2q^{18}-q^{16}+5q^{14}-7q^{12}+10q^{10}-12q^{8}+12q^{6}-11q^{4}+9q^{2}-6+3q^{-2}+q^{-4}-3q^{-6}+6q^{-8}-6q^{-10}+7q^{-12}-5q^{-14}+5q^{-16}-3q^{-18}+q^{-20}-q^{-22}$
1,0	$q^{56}-2q^{52}-2q^{50}+2q^{48}+4q^{46}-2q^{44}-5q^{42}+7q^{38}+4q^{36}-6q^{34}-6q^{32}+3q^{30}+6q^{28}-6q^{24}-2q^{22}+4q^{20}+3q^{18}-3q^{16}-3q^{14}+3q^{12}+4q^{10}-q^{8}-5q^{6}+6q^{2}+2-5q^{-2}-3q^{-4}+6q^{-6}+5q^{-8}-3q^{-10}-6q^{-12}+2q^{-14}+7q^{-16}+2q^{-18}-5q^{-20}-4q^{-22}+q^{-24}+4q^{-26}-2q^{-30}-q^{-32}+q^{-36}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{46}-2q^{44}+2q^{42}-4q^{40}+5q^{38}-5q^{36}+5q^{34}-5q^{32}+6q^{30}-3q^{28}+2q^{26}-q^{22}+2q^{20}-6q^{18}+6q^{16}-8q^{14}+8q^{12}-10q^{10}+9q^{8}-7q^{6}+10q^{4}-5q^{2}+6-q^{-2}+3q^{-4}+3q^{-6}-3q^{-8}+3q^{-10}-5q^{-12}+6q^{-14}-5q^{-16}+3q^{-18}-5q^{-20}+4q^{-22}-2q^{-24}+q^{-26}-q^{-28}+q^{-30}$

G2 Invariants.

Weight

Invariant

1,0

$q^{80}-2q^{78}+4q^{76}-7q^{74}+5q^{72}-2q^{70}-6q^{68}+16q^{66}-19q^{64}+20q^{62}-13q^{60}-4q^{58}+19q^{56}-29q^{54}+29q^{52}-14q^{50}-4q^{48}+20q^{46}-22q^{44}+16q^{42}-q^{40}-18q^{38}+23q^{36}-21q^{34}+7q^{32}+13q^{30}-31q^{28}+37q^{26}-24q^{24}+10q^{22}+6q^{20}-27q^{18}+34q^{16}-31q^{14}+22q^{12}-3q^{10}-15q^{8}+28q^{6}-23q^{4}+12q^{2}+4-18q^{-2}+20q^{-4}-13q^{-6}-q^{-8}+22q^{-10}-29q^{-12}+27q^{-14}-11q^{-16}-8q^{-18}+22q^{-20}-27q^{-22}+19q^{-24}-8q^{-26}+q^{-28}+8q^{-30}-12q^{-32}+8q^{-34}-3q^{-36}+2q^{-38}-2q^{-42}-q^{-44}+q^{-48}-q^{-50}+q^{-52}$

.

Computer Talk

The above data is available with the Mathematica package KnotTheory`, as shown in the (simulated) Mathematica session below. Your input (in red) is realistic; all else should have the same content as in a real mathematica session, but with different formatting. This Mathematica session is also available (albeit only for the knot 5_2) as the notebook PolynomialInvariantsSession.nb.

(The path below may be different on your system, and possibly also the KnotTheory` date)

In[1]:=

AppendTo[$Path, "C:/drorbn/projects/KAtlas/"]; << KnotTheory`

Loading KnotTheory` version of August 31, 2006, 11:25:27.5625. Read more at http://katlas.math.toronto.edu/wiki/KnotTheory.

In[3]:=

K = Knot["10 146"];

In[4]:=

Alexander[K][t]

KnotTheory::loading: Loading precomputed data in PD4Knots`.

Out[4]=

$2t^{2}-8t+13-8t^{-1}+2t^{-2}$

In[5]:=

Conway[K][z]

Out[5]=

$2z^{4}+1$

In[6]:=

Alexander[K, 2][t]

KnotTheory::credits: The program Alexander[K, r] to compute Alexander ideals was written by Jana Archibald at the University of Toronto in the summer of 2005.

Out[6]=

$\{1\}$

In[7]:=

{KnotDet[K], KnotSignature[K]}

Out[7]=

{ 33, 0 }

In[8]:=

Jones[K][q]

KnotTheory::loading: Loading precomputed data in Jones4Knots`.

Out[8]=

$-q^{3}+3q^{2}-4q+6-6q^{-1}+5q^{-2}-4q^{-3}+3q^{-4}-q^{-5}$

In[9]:=

HOMFLYPT[K][a, z]

KnotTheory::credits: The HOMFLYPT program was written by Scott Morrison.

Out[9]=

$-z^{2}a^{4}+z^{4}a^{2}+z^{2}a^{2}+z^{4}+z^{2}+1-z^{2}a^{-2}$

In[10]:=

Kauffman[K][a, z]

KnotTheory::loading: Loading precomputed data in Kauffman4Knots`.

Out[10]=

$a^{2}z^{8}+z^{8}+3a^{3}z^{7}+4az^{7}+z^{7}a^{-1}+3a^{4}z^{6}+a^{2}z^{6}-2z^{6}+a^{5}z^{5}-8a^{3}z^{5}-11az^{5}-2z^{5}a^{-1}-8a^{4}z^{4}-6a^{2}z^{4}+3z^{4}a^{-2}+5z^{4}-2a^{5}z^{3}+5a^{3}z^{3}+12az^{3}+6z^{3}a^{-1}+z^{3}a^{-3}+3a^{4}z^{2}+3a^{2}z^{2}-3z^{2}a^{-2}-3z^{2}-a^{3}z-3az-3za^{-1}-za^{-3}+1$

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n18, K11n62, ...}

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

Vassiliev invariants

V2 and V3:

(0, 0)

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 $0$ $0$ $0$ $-16$ $-16$ $0$ $0$ $32$ $-32$ $0$ $0$ $0$ $0$ $-8$ $-{\frac {32}{3}}$ ${\frac {64}{3}}$ $-{\frac {56}{3}}$ $-8$

V_2,1 through V_6,9 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 $t^{r}q^{j}$ are shown, along with their alternating sums $\chi$ (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=$0 is the signature of 10 146. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.

\   r    \    j   \ -5 -4 -3 -2 -1 0 1 2 3 χ 7                 1 -1 5               2   2 3             2 1   -1 1           4 2     2 -1         3 3       0 -3       2 3         -1 -5     2 3           1 -7   1 2             -1 -9   2               2 -11 1                 -1

Integral Khovanov Homology (db, data source)

$\dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}$ $i=-1$ $i=1$ $r=-5$ ${\mathbb {Z} }$ $r=-4$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}$ ${\mathbb {Z} }$ $r=-3$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=-2$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=-1$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{3}$ ${\mathbb {Z} }^{3}$ $r=0$ ${\mathbb {Z} }^{3}\oplus {\mathbb {Z} }_{2}^{3}$ ${\mathbb {Z} }^{4}$ $r=1$ ${\mathbb {Z} }^{2}\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=2$ ${\mathbb {Z} }\oplus {\mathbb {Z} }_{2}^{2}$ ${\mathbb {Z} }^{2}$ $r=3$ ${\mathbb {Z} }_{2}$ ${\mathbb {Z} }$

The Coloured Jones Polynomials

The Coloured Jones Polynomials (in the $n+1$-dimensional representation of $sl(2)$)

$n$	$J_{n}$
2	$-2q^{8}+3q^{7}+3q^{6}-11q^{5}+8q^{4}+12q^{3}-25q^{2}+8q+24-33q^{-1}+4q^{-2}+30q^{-3}-29q^{-4}-2q^{-5}+28q^{-6}-19q^{-7}-9q^{-8}+20q^{-9}-7q^{-10}-9q^{-11}+9q^{-12}-3q^{-14}+q^{-15}$
3	$q^{19}-q^{18}-q^{17}-3q^{16}+4q^{15}+8q^{14}-3q^{13}-17q^{12}-5q^{11}+33q^{10}+15q^{9}-42q^{8}-38q^{7}+53q^{6}+59q^{5}-52q^{4}-86q^{3}+53q^{2}+99q-39-116q^{-1}+33q^{-2}+118q^{-3}-19q^{-4}-117q^{-5}+7q^{-6}+110q^{-7}+7q^{-8}-99q^{-9}-22q^{-10}+83q^{-11}+36q^{-12}-64q^{-13}-44q^{-14}+40q^{-15}+50q^{-16}-20q^{-17}-45q^{-18}+2q^{-19}+35q^{-20}+8q^{-21}-22q^{-22}-13q^{-23}+13q^{-24}+9q^{-25}-4q^{-26}-5q^{-27}+3q^{-29}-q^{-30}$
4	$-q^{32}+q^{31}+3q^{30}-2q^{28}-10q^{27}-5q^{26}+16q^{25}+18q^{24}+13q^{23}-36q^{22}-57q^{21}+11q^{20}+64q^{19}+99q^{18}-30q^{17}-169q^{16}-81q^{15}+76q^{14}+262q^{13}+85q^{12}-265q^{11}-257q^{10}-20q^{9}+415q^{8}+286q^{7}-271q^{6}-413q^{5}-187q^{4}+475q^{3}+459q^{2}-204q-472-335q^{-1}+450q^{-2}+543q^{-3}-126q^{-4}-450q^{-5}-415q^{-6}+381q^{-7}+544q^{-8}-49q^{-9}-372q^{-10}-448q^{-11}+267q^{-12}+489q^{-13}+47q^{-14}-242q^{-15}-444q^{-16}+109q^{-17}+367q^{-18}+135q^{-19}-64q^{-20}-371q^{-21}-41q^{-22}+183q^{-23}+149q^{-24}+96q^{-25}-217q^{-26}-101q^{-27}+12q^{-28}+73q^{-29}+149q^{-30}-63q^{-31}-58q^{-32}-55q^{-33}-15q^{-34}+95q^{-35}+8q^{-36}+q^{-37}-36q^{-38}-36q^{-39}+31q^{-40}+8q^{-41}+14q^{-42}-6q^{-43}-16q^{-44}+4q^{-45}+5q^{-47}-3q^{-49}+q^{-50}$
5	$-2q^{46}+5q^{44}+5q^{43}-5q^{41}-22q^{40}-17q^{39}+15q^{38}+45q^{37}+49q^{36}+12q^{35}-76q^{34}-134q^{33}-71q^{32}+90q^{31}+239q^{30}+211q^{29}-37q^{28}-358q^{27}-443q^{26}-104q^{25}+444q^{24}+713q^{23}+383q^{22}-417q^{21}-1034q^{20}-774q^{19}+299q^{18}+1271q^{17}+1238q^{16}-9q^{15}-1457q^{14}-1706q^{13}-348q^{12}+1497q^{11}+2121q^{10}+774q^{9}-1458q^{8}-2435q^{7}-1150q^{6}+1296q^{5}+2649q^{4}+1503q^{3}-1150q^{2}-2744q-1730+942q^{-1}+2762q^{-2}+1932q^{-3}-798q^{-4}-2730q^{-5}-2016q^{-6}+627q^{-7}+2647q^{-8}+2093q^{-9}-474q^{-10}-2542q^{-11}-2118q^{-12}+303q^{-13}+2370q^{-14}+2138q^{-15}-92q^{-16}-2159q^{-17}-2122q^{-18}-146q^{-19}+1864q^{-20}+2067q^{-21}+410q^{-22}-1501q^{-23}-1946q^{-24}-663q^{-25}+1081q^{-26}+1737q^{-27}+859q^{-28}-633q^{-29}-1428q^{-30}-974q^{-31}+215q^{-32}+1063q^{-33}+946q^{-34}+127q^{-35}-658q^{-36}-816q^{-37}-339q^{-38}+298q^{-39}+586q^{-40}+418q^{-41}-20q^{-42}-349q^{-43}-360q^{-44}-142q^{-45}+125q^{-46}+255q^{-47}+190q^{-48}+11q^{-49}-125q^{-50}-150q^{-51}-88q^{-52}+25q^{-53}+101q^{-54}+89q^{-55}+18q^{-56}-35q^{-57}-60q^{-58}-47q^{-59}+9q^{-60}+36q^{-61}+29q^{-62}+6q^{-63}-8q^{-64}-18q^{-65}-14q^{-66}+6q^{-67}+9q^{-68}+3q^{-69}-5q^{-72}+3q^{-74}-q^{-75}$
6	$q^{68}-q^{67}-q^{66}-2q^{63}-3q^{62}+10q^{61}+8q^{60}+5q^{59}+2q^{58}-11q^{57}-36q^{56}-51q^{55}+2q^{54}+52q^{53}+90q^{52}+114q^{51}+60q^{50}-114q^{49}-288q^{48}-262q^{47}-84q^{46}+205q^{45}+546q^{44}+645q^{43}+206q^{42}-547q^{41}-1049q^{40}-1041q^{39}-388q^{38}+915q^{37}+1991q^{36}+1786q^{35}+248q^{34}-1692q^{33}-2968q^{32}-2693q^{31}-157q^{30}+3089q^{29}+4578q^{28}+3112q^{27}-593q^{26}-4539q^{25}-6351q^{24}-3522q^{23}+2249q^{22}+6962q^{21}+7300q^{20}+2819q^{19}-4116q^{18}-9482q^{17}-8029q^{16}-769q^{15}+7388q^{14}+10770q^{13}+7097q^{12}-1757q^{11}-10661q^{10}-11619q^{9}-4382q^{8}+6077q^{7}+12288q^{6}+10342q^{5}+1019q^{4}-10185q^{3}-13327q^{2}-7014q+4337+12253q^{-1}+11916q^{-2}+3013q^{-3}-9143q^{-4}-13633q^{-5}-8352q^{-6}+2987q^{-7}+11590q^{-8}+12374q^{-9}+4174q^{-10}-8078q^{-11}-13313q^{-12}-8999q^{-13}+1882q^{-14}+10654q^{-15}+12370q^{-16}+5123q^{-17}-6725q^{-18}-12568q^{-19}-9519q^{-20}+396q^{-21}+9107q^{-22}+12003q^{-23}+6335q^{-24}-4511q^{-25}-11000q^{-26}-9870q^{-27}-1796q^{-28}+6409q^{-29}+10771q^{-30}+7563q^{-31}-1310q^{-32}-8082q^{-33}-9319q^{-34}-4130q^{-35}+2602q^{-36}+8045q^{-37}+7763q^{-38}+1982q^{-39}-3984q^{-40}-7074q^{-41}-5221q^{-42}-1130q^{-43}+4071q^{-44}+6014q^{-45}+3720q^{-46}-115q^{-47}-3501q^{-48}-4123q^{-49}-3012q^{-50}+447q^{-51}+2891q^{-52}+3087q^{-53}+1745q^{-54}-378q^{-55}-1682q^{-56}-2487q^{-57}-1152q^{-58}+302q^{-59}+1223q^{-60}+1377q^{-61}+814q^{-62}+165q^{-63}-955q^{-64}-843q^{-65}-547q^{-66}-48q^{-67}+313q^{-68}+497q^{-69}+567q^{-70}-28q^{-71}-124q^{-72}-285q^{-73}-232q^{-74}-181q^{-75}+16q^{-76}+262q^{-77}+88q^{-78}+123q^{-79}-q^{-80}-38q^{-81}-141q^{-82}-96q^{-83}+45q^{-84}-2q^{-85}+63q^{-86}+39q^{-87}+38q^{-88}-36q^{-89}-40q^{-90}+q^{-91}-20q^{-92}+9q^{-93}+9q^{-94}+23q^{-95}-6q^{-96}-9q^{-97}+4q^{-98}-7q^{-99}+5q^{-102}-3q^{-104}+q^{-105}$
7	Not Available

Computer Talk

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

In[1]:=	<< KnotTheory`
Loading KnotTheory` (version of August 29, 2005, 15:27:48)...
In[2]:=	PD[Knot[10, 146]]
Out[2]=	PD[X[4, 2, 5, 1], X[5, 18, 6, 19], X[8, 3, 9, 4], X[2, 9, 3, 10], X[11, 17, 12, 16], X[7, 12, 8, 13], X[15, 6, 16, 7], X[17, 11, 18, 10], X[13, 1, 14, 20], X[19, 15, 20, 14]]
In[3]:=	GaussCode[Knot[10, 146]]
Out[3]=	GaussCode[1, -4, 3, -1, -2, 7, -6, -3, 4, 8, -5, 6, -9, 10, -7, 5, -8, 2, -10, 9]
In[4]:=	DTCode[Knot[10, 146]]
Out[4]=	DTCode[4, 8, -18, -12, 2, -16, -20, -6, -10, -14]
In[5]:=	br = BR[Knot[10, 146]]
Out[5]=	BR[4, {-1, -1, 2, -1, 2, 1, -3, 2, -1, 2, -3}]
In[6]:=	{First[br], Crossings[br]}
Out[6]=	{4, 11}
In[7]:=	BraidIndex[Knot[10, 146]]
Out[7]=	4
In[8]:=	Show[DrawMorseLink[Knot[10, 146]]]
Out[8]=	-Graphics-
In[9]:=	(#[Knot[10, 146]]&) /@ {SymmetryType, UnknottingNumber, ThreeGenus, BridgeIndex, SuperBridgeIndex, NakanishiIndex}
Out[9]=	{Reversible, 1, 2, 3, NotAvailable, 1}
In[10]:=	alex = Alexander[Knot[10, 146]][t]
Out[10]=	2 8 2 13 + -- - - - 8 t + 2 t 2 t t
In[11]:=	Conway[Knot[10, 146]][z]
Out[11]=	4 1 + 2 z
In[12]:=	Select[AllKnots[], (alex === Alexander[#][t])&]
Out[12]=	{Knot[10, 146], Knot[11, NonAlternating, 18], Knot[11, NonAlternating, 62]}
In[13]:=	{KnotDet[Knot[10, 146]], KnotSignature[Knot[10, 146]]}
Out[13]=	{33, 0}
In[14]:=	Jones[Knot[10, 146]][q]
Out[14]=	-5 3 4 5 6 2 3 6 - q + -- - -- + -- - - - 4 q + 3 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, 146]}
In[16]:=	A2Invariant[Knot[10, 146]][q]
Out[16]=	-16 -14 -12 -10 -8 -6 -2 2 4 6 8 10 -q + q + q - q + q - q + q + 2 q - q + q + q - q
In[17]:=	HOMFLYPT[Knot[10, 146]][a, z]
Out[17]=	2 2 z 2 2 4 2 4 2 4 1 + z - -- + a z - a z + z + a z 2 a
In[18]:=	Kauffman[Knot[10, 146]][a, z]
Out[18]=	2 3 z 3 z 3 2 3 z 2 2 4 2 z 1 - -- - --- - 3 a z - a z - 3 z - ---- + 3 a z + 3 a z + -- + 3 a 2 3 a a a 3 4 6 z 3 3 3 5 3 4 3 z 2 4 ---- + 12 a z + 5 a z - 2 a z + 5 z + ---- - 6 a z - a 2 a 5 4 4 2 z 5 3 5 5 5 6 2 6 4 6 8 a z - ---- - 11 a z - 8 a z + a z - 2 z + a z + 3 a z + a 7 z 7 3 7 8 2 8 -- + 4 a z + 3 a z + z + a z a
In[19]:=	{Vassiliev[2][Knot[10, 146]], Vassiliev[3][Knot[10, 146]]}
Out[19]=	{0, 0}
In[20]:=	Kh[Knot[10, 146]][q, t]
Out[20]=	3 1 2 1 2 2 3 2 - + 4 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 q t q t q t q t q t q t q t 3 3 3 3 2 5 2 7 3 ---- + --- + 2 q t + 2 q t + q t + 2 q t + q t 3 q t q t
In[21]:=	ColouredJones[Knot[10, 146], 2][q]
Out[21]=	-15 3 9 9 7 20 9 19 28 2 29 30 24 + q - --- + --- - --- - --- + -- - -- - -- + -- - -- - -- + -- + 14 12 11 10 9 8 7 6 5 4 3 q q q q q q q q q q q 4 33 2 3 4 5 6 7 8 -- - -- + 8 q - 25 q + 12 q + 8 q - 11 q + 3 q + 3 q - 2 q 2 q q

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10_145 10_147