80 research outputs found
Tutte and Jones polynomials of link families
This article contains general formulas for Tutte and Jones polynomials for
families of knots and links given in Conway notation and "portraits of
families"-- plots of zeroes of their corresponding Jones polynomials
Mirror-Curves and Knot Mosaics
Inspired by the paper on quantum knots and knot mosaics [23] and grid
diagrams (or arc presentations), used extensively in the computations of
Heegaard-Floer knot homology [2,3,7,24], we construct the more concise
representation of knot mosaics and grid diagrams via mirror-curves. Tame knot
theory is equivalent to knot mosaics [23], mirror-curves, and grid diagrams
[3,7,22,24]. Hence, we introduce codes for mirror-curves treated as knot or
link diagrams placed in rectangular square grids, suitable for software
implementation. We provide tables of minimal mirror-curve codes for knots and
links obtained from rectangular grids of size 3x3 and px2 (p<5), and describe
an efficient algorithm for computing the Kauffman bracket and L-polynomials
[18,19,20] directly from mirror-curve representations
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