On chain polynomials of geometric lattices
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917138386649088 |
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| author | Brändén, Petter Leite, Leonardo Saud Maia |
| author_facet | Brändén, Petter Leite, Leonardo Saud Maia |
| contents | Athanasiadis and Kalampogia-Evangelinou recently conjectured that the chain polynomial of any geometric lattice has only real zeros. We verify this conjecture for families of geometric lattices including perfect matroid designs, Dowling lattices, and for a class of geometric lattices that contains all lattices of flats of paving matroids. We also investigate how the conjecture behaves with respect to certain operations such as direct products, ordinal sums and single-element extensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13810 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On chain polynomials of geometric lattices Brändén, Petter Leite, Leonardo Saud Maia Combinatorics Athanasiadis and Kalampogia-Evangelinou recently conjectured that the chain polynomial of any geometric lattice has only real zeros. We verify this conjecture for families of geometric lattices including perfect matroid designs, Dowling lattices, and for a class of geometric lattices that contains all lattices of flats of paving matroids. We also investigate how the conjecture behaves with respect to certain operations such as direct products, ordinal sums and single-element extensions. |
| title | On chain polynomials of geometric lattices |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.13810 |