$f$-vector inequalities for order and chain polytopes
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929578079944704 |
|---|---|
| author | Freij-Hollanti, Ragnar Lundström, Teemu |
| author_facet | Freij-Hollanti, Ragnar Lundström, Teemu |
| contents | The order and chain polytopes are two 0/1-polytopes constructed from a finite poset. In this paper, we study the $f$-vectors of these polytopes. We investigate how the order and chain polytopes behave under disjoint unions and ordinal sums of posets, and how the $f$-vectors of these polytopes are expressed in terms of $f$-vectors of smaller polytopes. Our focus is on comparing the $f$-vectors of the order and chain polytope built from the same poset. In our main theorem we prove that for a family of posets built inductively by taking disjoint unions and ordinal sums of posets, for any poset $\mathcal{P}$ in this family the $f$-vector of the order polytope of $\mathcal{P}$ is component-wise at most the $f$-vector of the chain polytope of $\mathcal{P}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_13890 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $f$-vector inequalities for order and chain polytopes Freij-Hollanti, Ragnar Lundström, Teemu Combinatorics The order and chain polytopes are two 0/1-polytopes constructed from a finite poset. In this paper, we study the $f$-vectors of these polytopes. We investigate how the order and chain polytopes behave under disjoint unions and ordinal sums of posets, and how the $f$-vectors of these polytopes are expressed in terms of $f$-vectors of smaller polytopes. Our focus is on comparing the $f$-vectors of the order and chain polytope built from the same poset. In our main theorem we prove that for a family of posets built inductively by taking disjoint unions and ordinal sums of posets, for any poset $\mathcal{P}$ in this family the $f$-vector of the order polytope of $\mathcal{P}$ is component-wise at most the $f$-vector of the chain polytope of $\mathcal{P}$. |
| title | $f$-vector inequalities for order and chain polytopes |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2312.13890 |