L11a544
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a544's page at Knotilus. Visit L11a544's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11a544's Link Presentations]
| Planar diagram presentation | X6172 X12,4,13,3 X8,18,9,17 X14,8,15,7 X18,10,19,9 X10,12,5,11 X22,20,17,19 X16,22,11,21 X20,16,21,15 X2536 X4,14,1,13 |
| Gauss code | {1, -10, 2, -11}, {10, -1, 4, -3, 5, -6}, {6, -2, 11, -4, 9, -8}, {3, -5, 7, -9, 8, -7} |
| A Braid Representative |
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| A Morse Link Presentation | 
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[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...) | −v2u2 + vu2 + 2v2wu2−vwu2 + v2xu2−2vxu2−2v2wxu2 + 3vwxu2−wxu2 + xu2 + 2v2u−3vu−3v2wu + 3vwu−wu−v2xu + 3vxu + v2wxu−3vwxu + 2wxu−3xu + u−v2 + 3v + v2w−2vw + w−vx + vwx−wx + 2x−2 (db) |
| Jones polynomial |  (db)
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| Signature | 5 (db) |
| HOMFLY-PT polynomial | −z7a−5−z7a−7 + z5a−3−4z5a−5−3z5a−7 + z5a−9 + 4z3a−3−7z3a−5−z3a−7 + 2z3a−9 + 6za−3−10za−5 + 4za−7 + 4a−3z−1−9a−5z−1 + 6a−7z−1−a−9z−1 + a−3z−3−3a−5z−3 + 3a−7z−3−a−9z−3 (db) |
| Kauffman polynomial | −z10a−6−z10a−8−2z9a−5−7z9a−7−5z9a−9−2z8a−4−6z8a−6−14z8a−8−10z8a−10−z7a−3 + 7z7a−7−5z7a−9−11z7a−11 + 6z6a−4 + 22z6a−6 + 37z6a−8 + 13z6a−10−8z6a−12 + 5z5a−3 + 20z5a−5 + 28z5a−7 + 32z5a−9 + 15z5a−11−4z5a−13−2z4a−4−9z4a−6−17z4a−8−2z4a−10 + 7z4a−12−z4a−14−10z3a−3−36z3a−5−48z3a−7−32z3a−9−8z3a−11 + 2z3a−13−9z2a−4−18z2a−6−10z2a−8−2z2a−10−z2a−12 + 10za−3 + 27za−5 + 31za−7 + 16za−9 + 2za−11 + 10a−4 + 19a−6 + 10a−8−5a−3z−1−12a−5z−1−12a−7z−1−5a−9z−1−3a−4z−2−6a−6z−2−3a−8z−2 + a−3z−3 + 3a−5z−3 + 3a−7z−3 + a−9z−3 (db) |
[edit] 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 = 5 is the signature of L11a544. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11a544/KhovanovTable |
| Integral Khovanov Homology
(db, data source) |
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[edit] Computer Talk
Much of the above data can be recomputed by Mathematica using the packageKnotTheory`. See A Sample KnotTheory` Session.[edit] Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Link Page master template (intermediate). See/edit the Link_Splice_Base (expert). Back to the top. |
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