Multivariate Tutte polynomials of semimatroids
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909716308819968 |
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| author | Fu, Houshan |
| author_facet | Fu, Houshan |
| contents | We introduce and investigate multivariate Tutte polynomials, dichromatic polynomials, subset-corank polynomials, size-corank polynomials, and rank generating polynomials of semimatroids, which generalize the corresponding polynomial invariants of graphs and matroids. We primarily establish their deletion-contraction recurrences, basis activities expansions, and various convolution identities. These findings naturally extend Kook-Reiner-Stanton's convolution formula and Kung's convolution-multiplication identities for the Tutte polynomials of graphs and matroids to semimatroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00561 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multivariate Tutte polynomials of semimatroids Fu, Houshan Combinatorics 05C31, 05B35 We introduce and investigate multivariate Tutte polynomials, dichromatic polynomials, subset-corank polynomials, size-corank polynomials, and rank generating polynomials of semimatroids, which generalize the corresponding polynomial invariants of graphs and matroids. We primarily establish their deletion-contraction recurrences, basis activities expansions, and various convolution identities. These findings naturally extend Kook-Reiner-Stanton's convolution formula and Kung's convolution-multiplication identities for the Tutte polynomials of graphs and matroids to semimatroids. |
| title | Multivariate Tutte polynomials of semimatroids |
| topic | Combinatorics 05C31, 05B35 |
| url | https://arxiv.org/abs/2508.00561 |