L11a42
From Knot Atlas



(Knotscape image) 
See the full Thistlethwaite Link Table (up to 11 crossings).
Visit L11a42's page at Knotilus. Visit L11a42's page at the original Knot Atlas. 
Link Presentations
[edit Notes on L11a42's Link Presentations]
Planar diagram presentation  X_{6172} X_{10,4,11,3} X_{18,8,19,7} X_{20,13,21,14} X_{22,15,5,16} X_{14,21,15,22} X_{16,19,17,20} X_{12,10,13,9} X_{8,18,9,17} X_{2536} X_{4,12,1,11} 
Gauss code  {1, 10, 2, 11}, {10, 1, 3, 9, 8, 2, 11, 8, 4, 6, 5, 7, 9, 3, 7, 4, 6, 5} 
A Braid Representative   
A Morse Link Presentation 
Polynomial invariants
Multivariable Alexander Polynomial (in , , , ...)  (db) 
Jones polynomial  (db) 
Signature  1 (db) 
HOMFLYPT polynomial  (db) 
Kauffman polynomial  (db) 
Khovanov Homology
The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where 1 is the signature of L11a42. Nonzero entries off the critical diagonals (if any exist) are highlighted in red. 

Integral Khovanov Homology
(db, data source) 

Computer Talk
Much of the above data can be recomputed by Mathematica using the package KnotTheory`
. See A Sample KnotTheory` Session.
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. 
