$f$-vector inequalities for order and chain polytopes

Authors

  • Ragnar Freij-Hollanti
  • Teemu Lundström

DOI:

https://doi.org/10.7146/math.scand.a-143995

Abstract

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 $\mathcal {P}$.

References

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Published

2024-11-04

How to Cite

Freij-Hollanti, R., & Lundström, T. (2024). $f$-vector inequalities for order and chain polytopes. MATHEMATICA SCANDINAVICA, 130(3). https://doi.org/10.7146/math.scand.a-143995

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Section

Articles