L10n100
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L10n100's page at Knotilus. Visit L10n100's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L10n100's Link Presentations]
| Planar diagram presentation | X6172 X3,11,4,10 X7,15,8,14 X13,5,14,8 X11,18,12,19 X20,16,17,15 X16,20,9,19 X17,12,18,13 X2536 X9,1,10,4 |
| Gauss code | {1, -9, -2, 10}, {9, -1, -3, 4}, {-8, 5, 7, -6}, {-10, 2, -5, 8, -4, 3, 6, -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, ...) | −vu + vwu−wu + vxu−vwxu + wxu−xu + u + v−vw + w−vx + vwx−wx + x−1 (db) |
| Jones polynomial |  (db)
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| Signature | 1 (db) |
| HOMFLY-PT polynomial | z5a−1−az3 + 2z3a−1−z3a−3−za−1 + za−3 + 2az−1−5a−1z−1 + 4a−3z−1−a−5z−1 + az−3−3a−1z−3 + 3a−3z−3−a−5z−3 (db) |
| Kauffman polynomial | −z7a−1−z7a−3−5z6a−2−z6a−4−4z6−4az5−6z5a−1−2z5a−3−a2z4 + 6z4a−2 + 5z4 + 6az3 + 10z3a−1 + z3a−3−3z3a−5−6z2a−2−5z2a−4−z2 + za−1 + 5za−3 + 4za−5 + 11a−2 + 6a−4 + 6−3az−1−6a−1z−1−6a−3z−1−3a−5z−1−6a−2z−2−3a−4z−2−3z−2 + az−3 + 3a−1z−3 + 3a−3z−3 + a−5z−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 = 1 is the signature of L10n100. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L10n100/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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