From Knot Atlas
[edit] Link Presentations
[edit Notes on L9a15's Link Presentations]
| Planar diagram presentation
| X6172 X12,4,13,3 X14,8,15,7 X18,12,5,11 X8,18,9,17 X16,10,17,9 X10,16,11,15 X2536 X4,14,1,13
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| Gauss code
| {1, -8, 2, -9}, {8, -1, 3, -5, 6, -7, 4, -2, 9, -3, 7, -6, 5, -4}
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[edit] Polynomial invariants
| Multivariable Alexander Polynomial (in u, v, w, ...)
| −2vu3 + 2u3 + 3vu2−3u2−3vu + 3u + 2v−2 (db)
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| Jones polynomial
|  (db)
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| Signature
| 3 (db)
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| HOMFLY-PT polynomial
| −z5a−3−z5a−5 + z3a−1−2z3a−3−3z3a−5 + z3a−7 + 2za−1−4za−5 + 2za−7 + a−1z−1−2a−5z−1 + a−7z−1 (db)
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| Kauffman polynomial
| −z8a−4−z8a−6−2z7a−3−5z7a−5−3z7a−7−2z6a−2−2z6a−4−3z6a−6−3z6a−8−z5a−1 + 2z5a−3 + 12z5a−5 + 7z5a−7−2z5a−9 + 4z4a−2 + 8z4a−4 + 11z4a−6 + 6z4a−8−z4a−10 + 3z3a−1 + 3z3a−3−13z3a−5−10z3a−7 + 3z3a−9−7z2a−4−15z2a−6−6z2a−8 + 2z2a−10−3za−1 + 7za−5 + 4za−7−a−2 + 3a−4 + 5a−6 + 2a−8 + a−1z−1−2a−5z−1−a−7z−1 (db)
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| 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 L9a15. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
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| Data:L9a15/KhovanovTable
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