L11a490
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a490's page at Knotilus. Visit L11a490's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11a490's Link Presentations]
| Planar diagram presentation | X6172 X10,3,11,4 X22,16,19,15 X20,8,21,7 X8,20,9,19 X18,14,5,13 X14,12,15,11 X12,18,13,17 X16,22,17,21 X2536 X4,9,1,10 |
| Gauss code | {1, -10, 2, -11}, {5, -4, 9, -3}, {10, -1, 4, -5, 11, -2, 7, -8, 6, -7, 3, -9, 8, -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, ...) |  (db)
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| Jones polynomial | −q8 + 3q7−7q6 + 13q5−18q4 + 21q3 + q−3−20q2−3q−2 + 19q + 9q−1−13 (db) |
| Signature | 2 (db) |
| HOMFLY-PT polynomial | −a−8 + 3z2a−6−a−6z−2 + 2a−6−3z4a−4−2z2a−4 + 4a−4z−2 + 4a−4 + z6a−2 + a2z2−5z2a−2−5a−2z−2 + a2−9a−2−2z4−z2 + 2z−2 + 3 (db) |
| Kauffman polynomial | z5a−9−2z3a−9 + za−9 + 3z6a−8−5z4a−8 + 3z2a−8−a−8 + 5z7a−7−6z5a−7 + 3z3a−7−2za−7 + a−7z−1 + 6z8a−6−5z6a−6−z4a−6 + 4z2a−6−a−6z−2 + 4z9a−5 + 7z7a−5−29z5a−5 + 37z3a−5−21za−5 + 5a−5z−1 + z10a−4 + 16z8a−4−38z6a−4 + 35z4a−4−22z2a−4−4a−4z−2 + 14a−4 + 8z9a−3 + 3z7a−3−48z5a−3 + 68z3a−3−41za−3 + 9a−3z−1 + z10a−2 + 16z8a−2 + a2z6−46z6a−2−3a2z4 + 52z4a−2 + 3a2z2−44z2a−2−5a−2z−2−a2 + 23a−2 + 4z9a−1 + 3az7 + 4z7a−1−6az5−32z5a−1 + 3az3 + 39z3a−1−23za−1 + 5a−1z−1 + 6z8−15z6 + 18z4−18z2−2z−2 + 10 (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 = 2 is the signature of L11a490. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11a490/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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