Classification and Ehrhart Theory of Denominator 2 Polygons
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929608505425920 |
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| author | Hamm, Girtrude Hofscheier, Johannes Kasprzyk, Alexander |
| author_facet | Hamm, Girtrude Hofscheier, Johannes Kasprzyk, Alexander |
| contents | We present an algorithm for growing the denominator $r$ polygons containing a fixed number of lattice points and enumerate such polygons containing few lattice points for small $r$. We describe the Ehrhart quasi-polynomial of a rational polygon in terms of boundary and interior point counts. Using this, we bound the coefficients of Ehrhart quasi-polynomials of denominator 2 polygons. In particular, we completely classify such polynomials in the case of zero interior points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classification and Ehrhart Theory of Denominator 2 Polygons Hamm, Girtrude Hofscheier, Johannes Kasprzyk, Alexander Combinatorics We present an algorithm for growing the denominator $r$ polygons containing a fixed number of lattice points and enumerate such polygons containing few lattice points for small $r$. We describe the Ehrhart quasi-polynomial of a rational polygon in terms of boundary and interior point counts. Using this, we bound the coefficients of Ehrhart quasi-polynomials of denominator 2 polygons. In particular, we completely classify such polynomials in the case of zero interior points. |
| title | Classification and Ehrhart Theory of Denominator 2 Polygons |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2411.19183 |