Inequalities for Chow Polynomials and Chern Numbers of Matroids
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917446638632960 |
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| author | Cheng, Ronnie Lin, Wangyang |
| author_facet | Cheng, Ronnie Lin, Wangyang |
| contents | The Chow polynomial of a matroid is a fundamental invariant whose coefficients exhibit strong positivity properties, including $γ$-positivity. We interpret the normalized Chow coefficients as a probability distribution and establish new inequalities for its central moments. As consequences, we obtain bounds on the number of flags of flats and inequalities on the roots of the Chow polynomial.
We further relate these moment inequalities to algebraic geometry via the Hirzebruch $χ_y$-genus. This yields new inequalities for matroidal Chern numbers. In particular, for any matroid of rank $d+1$, we prove that $c_1c_{d-1}\le c_d$, with equality if and only if $d=1$ or the simplification of the matroid is Boolean. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities for Chow Polynomials and Chern Numbers of Matroids Cheng, Ronnie Lin, Wangyang Combinatorics Algebraic Geometry 05B35, 14C17, 05A20, 60C05 The Chow polynomial of a matroid is a fundamental invariant whose coefficients exhibit strong positivity properties, including $γ$-positivity. We interpret the normalized Chow coefficients as a probability distribution and establish new inequalities for its central moments. As consequences, we obtain bounds on the number of flags of flats and inequalities on the roots of the Chow polynomial. We further relate these moment inequalities to algebraic geometry via the Hirzebruch $χ_y$-genus. This yields new inequalities for matroidal Chern numbers. In particular, for any matroid of rank $d+1$, we prove that $c_1c_{d-1}\le c_d$, with equality if and only if $d=1$ or the simplification of the matroid is Boolean. |
| title | Inequalities for Chow Polynomials and Chern Numbers of Matroids |
| topic | Combinatorics Algebraic Geometry 05B35, 14C17, 05A20, 60C05 |
| url | https://arxiv.org/abs/2603.21680 |