L11a542
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a542's page at Knotilus. Visit L11a542's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11a542's Link Presentations]
| Planar diagram presentation | X6172 X12,6,13,5 X8493 X2,16,3,15 X16,7,17,8 X22,20,15,19 X14,22,11,21 X20,14,21,13 X18,10,19,9 X10,12,5,11 X4,17,1,18 |
| Gauss code | {1, -4, 3, -11}, {10, -2, 8, -7}, {2, -1, 5, -3, 9, -10}, {4, -5, 11, -9, 6, -8, 7, -6} |
| 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 + 2vu2 + 2v2wu2−3vwu2 + wu2 + v2xu2−2vxu2−2v2wxu2 + 3vwxu2−wxu2 + xu2−u2 + 2v2u−5vu−3v2wu + 5vwu−2wu−2v2xu + 5vxu + 3v2wxu−5vwxu + 2wxu−3xu + 3u−v2 + 3v + v2w−2vw + w + v2x−3vx−v2wx + 2vwx−wx + 2x−2 (db) |
| Jones polynomial |  (db)
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| Signature | 3 (db) |
| HOMFLY-PT polynomial | z7a−3 + z7a−5−z5a−1 + 3z5a−3 + 2z5a−5−z5a−7−2z3a−1 + 4z3a−3−z3a−5−z3a−7 + 2za−3−3za−5 + za−7 + 2a−1z−1−4a−3z−1 + 2a−5z−1 + a−1z−3−3a−3z−3 + 3a−5z−3−a−7z−3 (db) |
| Kauffman polynomial | −2z10a−4−2z10a−6−5z9a−3−13z9a−5−8z9a−7−6z8a−2−15z8a−4−22z8a−6−13z8a−8−4z7a−1−4z7a−3 + 5z7a−5−6z7a−7−11z7a−9 + 9z6a−2 + 32z6a−4 + 43z6a−6 + 16z6a−8−5z6a−10−z6 + 10z5a−1 + 30z5a−3 + 35z5a−5 + 31z5a−7 + 15z5a−9−z5a−11−9z4a−4−14z4a−6−3z4a−8 + 4z4a−10 + 2z4−10z3a−1−32z3a−3−36z3a−5−20z3a−7−6z3a−9−3z2a−2−4z2a−4−3z2a−6−z2a−8−z2 + 3za−1 + 11za−3 + 11za−5 + 3za−7−4a−2−7a−4−4a−6 + 2a−1z−1 + 3a−3z−1 + 3a−5z−1 + 2a−7z−1 + 3a−2z−2 + 6a−4z−2 + 3a−6z−2−a−1z−3−3a−3z−3−3a−5z−3−a−7z−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 = 3 is the signature of L11a542. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11a542/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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