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This article is cited in 1 scientific paper (total in 1 paper)
Transition polynomial as a weight system for binary delta-matroids
Alexander Dunaykin, Vyacheslav Zhukov International Laboratory of Cluster Geometry National Research University Higher School of Economics
Abstract:
To a singular knot $K$ with $n$ double points, one can associate a chord diagram with $n$ chords. A chord diagram can also be understood as a $4$-regular graph endowed with an oriented Euler circuit. L. Traldi introduced a polynomial invariant for such graphs, called a transition polynomial. We specialize this polynomial to a multiplicative weight system, that is, a function on chord diagrams satisfying $4$-term relations and determining thus a finite type knot invariant. We prove a similar statement for the transition polynomial of general ribbon graphs and binary delta-matroids defined by R. Brijder and H. J. Hoogeboom, which defines, as a consequence, a finite type invariant of links.
Key words and phrases:
knot, link, finite type invariant of knots, chord diagram, transition polynomial, delta-matroid.
Citation:
Alexander Dunaykin, Vyacheslav Zhukov, “Transition polynomial as a weight system for binary delta-matroids”, Mosc. Math. J., 22:1 (2022), 69–81
Linking options:
https://www.mathnet.ru/eng/mmj816 https://www.mathnet.ru/eng/mmj/v22/i1/p69
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