L9a26
From Knot Atlas
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 (Knotscape image) | See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L9a26's page at Knotilus. Visit L9a26's page at the original Knot Atlas. |
[edit] Link Presentations
[edit Notes on L9a26's Link Presentations]
| Planar diagram presentation | X8192 X10,4,11,3 X18,10,7,9 X14,6,15,5 X16,14,17,13 X12,18,13,17 X2738 X4,12,5,11 X6,16,1,15 |
| Gauss code | {1, -7, 2, -8, 4, -9}, {7, -1, 3, -2, 8, -6, 5, -4, 9, -5, 6, -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, ...) | −2v2u2 + 3vu2−u2 + 3v2u−5vu + 3u−v2 + 3v−2 (db) |
| Jones polynomial |  (db)
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| Signature | 3 (db) |
| HOMFLY-PT polynomial | −z5a−3−z5a−5 + z3a−1−2z3a−3−2z3a−5 + z3a−7 + 2za−1−za−3−za−5 + za−7 + a−1z−1−a−3z−1 (db) |
| Kauffman polynomial | −z8a−4−z8a−6−2z7a−3−5z7a−5−3z7a−7−2z6a−2−3z6a−4−5z6a−6−4z6a−8−z5a−1 + z5a−3 + 6z5a−5 + z5a−7−3z5a−9 + 4z4a−2 + 7z4a−4 + 9z4a−6 + 5z4a−8−z4a−10 + 3z3a−1 + 5z3a−3 + 2z3a−7 + 4z3a−9−z2a−2−2z2a−4−4z2a−6−2z2a−8 + z2a−10−3za−1−4za−3−za−5−za−7−za−9−a−2 + a−1z−1 + a−3z−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 = 3 is the signature of L9a26. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. | Data:L9a26/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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