L11a132
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a132's page at Knotilus. Visit L11a132's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11a132's Link Presentations]
| Planar diagram presentation | X6172 X14,4,15,3 X22,8,5,7 X20,10,21,9 X18,12,19,11 X16,14,17,13 X12,18,13,17 X10,20,11,19 X8,22,9,21 X2536 X4,16,1,15 |
| Gauss code | {1, -10, 2, -11}, {10, -1, 3, -9, 4, -8, 5, -7, 6, -2, 11, -6, 7, -5, 8, -4, 9, -3} |
| 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, ...) | −4vu + 4u + 4v−4 (db) |
| Jones polynomial |  (db)
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| Signature | 1 (db) |
| HOMFLY-PT polynomial | −z3a−1−z3a−3−z3a−5−z3a−7 + az−za−1−za−7 + za−9 + az−1−a−1z−1 (db) |
| Kauffman polynomial | −z10a−6−z10a−8−z9a−5−3z9a−7−2z9a−9−z8a−4 + 5z8a−6 + 5z8a−8−z8a−10−z7a−3 + 3z7a−5 + 17z7a−7 + 13z7a−9−z6a−2 + 2z6a−4−9z6a−6−6z6a−8 + 6z6a−10−z5a−1 + z5a−3−z5a−5−29z5a−7−26z5a−9 + 10z4a−6 + z4a−8−10z4a−10−z4−az3−z3a−1 + 17z3a−7 + 17z3a−9−4z2a−6 + 4z2a−10 + 2az + 2za−1−2za−7−2za−9 + 1−az−1−a−1z−1 (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 L11a132. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11a132/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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