Transition polynomial as a weight system for binary delta-matroids
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866909797933121536 |
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| author | Dunaykin, Alexander Zhukov, Vyacheslav |
| author_facet | Dunaykin, Alexander Zhukov, Vyacheslav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_03831 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Transition polynomial as a weight system for binary delta-matroids Dunaykin, Alexander Zhukov, Vyacheslav Combinatorics 05C31 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. |
| title | Transition polynomial as a weight system for binary delta-matroids |
| topic | Combinatorics 05C31 |
| url | https://arxiv.org/abs/1907.03831 |