On facet gaps of order and chain polytopes

Ghislain Fourier

arXiv:2608.19989v1 Primary: math.CO

Abstract

We discuss three questions from a recent paper of Bhandari, Cunningham, Morrell, Oh and Smith. We obtain an exact local formula for the facet gap between the order and the chain polytope of a finite poset. This gives a classification of the case $\gap(P)=2$ in terms of star elements. For marked chain--order polytopes, the same local weights determine the facet differences between all admissible decompositions.

Disclosure

“]. Acknowledgment. The author gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Symbolic Tools in Math- ematics and their Application (TRR 195, project-ID 286237555). ChatGPT (OpenAI) was used for language editing and for computations in examples. 2. The facet gap and star elements We add a smallest element b 1 to P and write Pb = P ⊔ {b”
PDF page 2

Classification: Computational experiments or data processing
Multiplier: 3
Verified: 2026-08-22T18:11:39.019754Z

Structural counts

Pages 6 pdf

Theorems 1 source

Lemmas 0 source

Propositions 1 source

Corollaries 1 source

Definitions 0 source

Displayed equations 33 source

Bibliography entries 27 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file main__1_.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.