# Enriched chain polytopes

@article{Ohsugi2018EnrichedCP, title={Enriched chain polytopes}, author={Hidefumi Ohsugi and Akiyoshi Tsuchiya}, journal={Israel Journal of Mathematics}, year={2018}, volume={237}, pages={485-500} }

Stanley introduced a lattice polytope $$\mathscr{C}_P$$ C P arising from a finite poset P , which is called the chain polytope of P . The geometric structure of $$\mathscr{C}_P$$ C P has good relations with the combinatorial structure of P . In particular, the Ehrhart polynomial of $$\mathscr{C}_P$$ C P is given by the order polynomial of P . In the present paper, associated to P , we introduce a lattice polytope ℰ P , which is called the enriched chain polytope of P , and investigate geometric…

## 5 Citations

Enriched order polytopes and enriched Hibi rings

- MathematicsEuropean Journal of Mathematics
- 2020

Stanley introduced two classes of lattice polytopes associated to posets, which are called the order polytope $${{\mathscr {O}}}_P$$ O P and the chain polytope $${{\mathscr {C}}}_P$$ C P of a poset P…

Two poset polytopes are mutation-equivalent

- Mathematics
- 2020

The combinatorial mutation $\mathrm{mut}_w(P,F)$ for a lattice polytope $P$ was introduced in the context of mirror symmetry for Fano manifolds in [1]. It was also proved in [1] that for a lattice…

Two enriched poset polytopes

- Mathematics
- 2020

Stanley introduced and studied two lattice polytopes, the order polytope and chain polytope, associated to a finite poset. Recently Ohsugi and Tsuchiya introduce an enriched version of them, called…

Unconditional Reflexive Polytopes

- MathematicsDiscret. Comput. Geom.
- 2020

This work derives constructions for Gale-dual pairs of polytopes and explicitly describes Gröbner bases for unconditional reflexive poly topes coming from partially ordered sets in terms of perfect graphs.

The h*-Polynomials of Locally Anti-Blocking Lattice Polytopes and Their γ-Positivity

- MathematicsDiscret. Comput. Geom.
- 2021

A formula for the -polynomials of locally anti-blocking lattice polytopes is given and the -positivity ofh is discussed, which is unimodularly equivalent to an anti- blocking polytope by reflections of coordinate hyperplanes.

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