L11n143
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11n143's page at Knotilus. Visit L11n143's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L11n143's Link Presentations]
| Planar diagram presentation | X8192 X11,19,12,18 X3,10,4,11 X17,3,18,2 X12,5,13,6 X6718 X16,10,17,9 X20,16,21,15 X22,14,7,13 X14,22,15,21 X4,20,5,19 |
| Gauss code | {1, 4, -3, -11, 5, -6}, {6, -1, 7, 3, -2, -5, 9, -10, 8, -7, -4, 2, 11, -8, 10, -9} |
| 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, ...) | −2v2u2 + 2vu2−vu + 2v−2 (db) |
| Jones polynomial |  (db)
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| Signature | -1 (db) |
| HOMFLY-PT polynomial | −z5a−1−z5a−3 + az3−4z3a−1−4z3a−3 + z3a−5 + 3az−3za−1−4za−3 + 3za−5 + az−1−2a−3z−1 + a−5z−1 (db) |
| Kauffman polynomial | −z9a−3−z9a−5−2z8a−2−3z8a−4−z8a−6−2z7a−1 + 4z7a−3 + 6z7a−5 + 10z6a−2 + 18z6a−4 + 7z6a−6−z6 + 9z5a−1−2z5a−3−11z5a−5−14z4a−2−33z4a−4−16z4a−6 + 3z4−2az3−10z3a−1 + 8z3a−5−a2z2 + 9z2a−2 + 22z2a−4 + 13z2a−6−z2−a3z + 4az + 4za−1−5za−3−4za−5−3a−2−5a−4−2a−6 + 1−az−1 + 2a−3z−1 + a−5z−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 L11n143. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L11n143/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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