On the enumeration of series-parallel matroids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917805576683520 |
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| author | Proudfoot, Nicholas Xu, Yuan Young, Ben |
| author_facet | Proudfoot, Nicholas Xu, Yuan Young, Ben |
| contents | By the work of Ferroni and Larson, Kazhdan-Lusztig polynomials and Z-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of series-parallel matroids and the number of simple series-parallel matroids of a given rank and cardinality, extending results of Ferroni-Larson and Gao-Proudfoot-Yang-Zhang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the enumeration of series-parallel matroids Proudfoot, Nicholas Xu, Yuan Young, Ben Combinatorics 05A15, 05B35 By the work of Ferroni and Larson, Kazhdan-Lusztig polynomials and Z-polynomials of complete graphs have combinatorial interpretations in terms of quasi series-parallel matroids. We provide explicit formulas for the number of series-parallel matroids and the number of simple series-parallel matroids of a given rank and cardinality, extending results of Ferroni-Larson and Gao-Proudfoot-Yang-Zhang. |
| title | On the enumeration of series-parallel matroids |
| topic | Combinatorics 05A15, 05B35 |
| url | https://arxiv.org/abs/2406.04502 |