On the number of faces of marked order polytopes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918096991682560 |
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| author | Melikhova, Ekaterina V. |
| author_facet | Melikhova, Ekaterina V. |
| contents | In this paper, we present a new method for computing the f-vector of a marked order polytope. Namely, given an arbitrary (polyhedral) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field Z_2) such that the dimensions of its cohomology groups equal the components of the f-vector of the original polytope. In the case of a marked order polytope and its well-known cubosimplicial subdivision, this cochain complex can be described purely combinatorially -- which yields the said computation of the f-vector. Of independent interest may be our combinatorial description of the said cubosimplicial subdivision (which was originally constructed geometrically). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the number of faces of marked order polytopes Melikhova, Ekaterina V. Combinatorics Metric Geometry In this paper, we present a new method for computing the f-vector of a marked order polytope. Namely, given an arbitrary (polyhedral) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field Z_2) such that the dimensions of its cohomology groups equal the components of the f-vector of the original polytope. In the case of a marked order polytope and its well-known cubosimplicial subdivision, this cochain complex can be described purely combinatorially -- which yields the said computation of the f-vector. Of independent interest may be our combinatorial description of the said cubosimplicial subdivision (which was originally constructed geometrically). |
| title | On the number of faces of marked order polytopes |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2507.13596 |