Counting Lattice Points in Generalized Permutohedra From A to B
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912740544610304 |
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| author | Thawinrak, Warut |
| author_facet | Thawinrak, Warut |
| contents | We derive a formula for the number of lattice points in type B generalized permutohedra, providing a concise alternative to the formula obtained recently by Eur, Fink, Larson, and Spink as a result from a study of delta-matroids. Our approach builds upon the existing framework and techniques introduced by Postnikov in his work on type A generalized permutohedra, a family of polytopes interconnected with many mathematical concepts such as matroids and Weyl groups. In particular, we express the number of lattice points in type B generalized permutohedra in terms of Postnikov's notion of G-draconian sequences, from which their Ehrhart polynomials and volume formula follow as consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01332 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Counting Lattice Points in Generalized Permutohedra From A to B Thawinrak, Warut Combinatorics We derive a formula for the number of lattice points in type B generalized permutohedra, providing a concise alternative to the formula obtained recently by Eur, Fink, Larson, and Spink as a result from a study of delta-matroids. Our approach builds upon the existing framework and techniques introduced by Postnikov in his work on type A generalized permutohedra, a family of polytopes interconnected with many mathematical concepts such as matroids and Weyl groups. In particular, we express the number of lattice points in type B generalized permutohedra in terms of Postnikov's notion of G-draconian sequences, from which their Ehrhart polynomials and volume formula follow as consequences. |
| title | Counting Lattice Points in Generalized Permutohedra From A to B |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.01332 |