Experimental Mathematics 20-3 (2011) 282-287
last updated Sun, 14 Apr 2013 11:23:03 -0400
first edition: September 28, 2009
Abstract. We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every weight system integrates".
The paper. v-Dims.pdf (source: v-Dims.zip), arXiv:0909.5169.
|dim Vn/n-1 / dim Wn for ...||round v-knots||long v-knots||descending v-knots|
|standard R23||mod R1||0,0,1,4,17||0,2,7,42,246||0,0,1,6,34|
|braid-like R23||mod R1||0,0,1,4,17||0,2,7,42,246||0,0,1,6,34|
|R2 only||mod R1||0,0,4,44,648||0,2,28,420,7808||0,0,2,18,174|
Related Mathematica Notebooks. "PolyakAlgebra" (Source, PDF), "PolyakAlgebraOnSphere" (Source, PDF).
Related Talks (with video). "18 Conjectures", day 3 of Talks: Goettingen-1004 and day 2 of Talks: Chicago-1009.
Related Scratch Work is under GPV.
September 2009 Version. v-Dims-090928.pdf (source: v-Dims-090928.zip).