Schubert matroids, Delannoy paths, and Speyer's invariant
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916089012682752 |
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| author | Ferroni, Luis |
| author_facet | Ferroni, Luis |
| contents | We provide a combinatorial way of computing Speyer's $g$-polynomial on arbitrary Schubert matroids via the enumeration of certain Delannoy paths. We define a new statistic of a basis in a matroid, and express the $g$-polynomial of a Schubert matroid in terms of it and internal and external activities. Some surprising positivity properties of the $g$-polynomial of Schubert matroids are deduced from our expression. Finally, we combine our formulas with a fundamental result of Derksen and Fink to provide an algorithm for computing the $g$-polynomial of an arbitrary matroid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01397 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schubert matroids, Delannoy paths, and Speyer's invariant Ferroni, Luis Combinatorics We provide a combinatorial way of computing Speyer's $g$-polynomial on arbitrary Schubert matroids via the enumeration of certain Delannoy paths. We define a new statistic of a basis in a matroid, and express the $g$-polynomial of a Schubert matroid in terms of it and internal and external activities. Some surprising positivity properties of the $g$-polynomial of Schubert matroids are deduced from our expression. Finally, we combine our formulas with a fundamental result of Derksen and Fink to provide an algorithm for computing the $g$-polynomial of an arbitrary matroid. |
| title | Schubert matroids, Delannoy paths, and Speyer's invariant |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2311.01397 |