Dowling's polynomial conjecture for independent sets of matroids
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918300970123264 |
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| author | Cao, Shiqi Chen, Keyi Li, Yitian Wu, Yuxin |
| author_facet | Cao, Shiqi Chen, Keyi Li, Yitian Wu, Yuxin |
| contents | The celebrated Mason's conjecture states that the sequence of independent set numbers of any matroid is log-concave, and even ultra log-concave. The strong form of Mason's conjecture was independently solved by Anari, Liu, Oveis Gharan and Vinzant, and by Brändén and Huh. The weak form of Mason's conjecture was also generalized to a polynomial version by Dowling in 1980 by considering certain polynomial analogue of independent set numbers. In this paper we completely solve Dowling's polynomial conjecture by using the theory of Lorentzian polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03809 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dowling's polynomial conjecture for independent sets of matroids Cao, Shiqi Chen, Keyi Li, Yitian Wu, Yuxin Combinatorics The celebrated Mason's conjecture states that the sequence of independent set numbers of any matroid is log-concave, and even ultra log-concave. The strong form of Mason's conjecture was independently solved by Anari, Liu, Oveis Gharan and Vinzant, and by Brändén and Huh. The weak form of Mason's conjecture was also generalized to a polynomial version by Dowling in 1980 by considering certain polynomial analogue of independent set numbers. In this paper we completely solve Dowling's polynomial conjecture by using the theory of Lorentzian polynomials. |
| title | Dowling's polynomial conjecture for independent sets of matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.03809 |