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… 
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References

SHOWING 1-10 OF 27 REFERENCES
h-Vectors of Gorenstein polytopes
Reflexive polytopes arising from bipartite graphs with $$\gamma $$-positivity associated to interior polynomials
In this paper, we introduce polytopes $${\mathscr {B}}_G$$ arising from root systems $$B_n$$ and finite graphs G, and study their combinatorial and algebraic properties. In particular, it is
Minuscule Schubert Varieties: Poset Polytopes, PBW-Degenerated Demazure Modules, and Kogan Faces
We study a family of posets and the associated chain and order polytopes. We identify the order polytope as a maximal Kogan face in a Gelfand-Tsetlin polytope of a multiple of a fundamental weight.
Two poset polytopes
TLDR
A transfer map allows us to transfer properties of ϑ(P) to ℒ(P), and to transfer known inequalities involving linear extensions ofP to some new inequalities.
Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
Abstract A lattice polytope is a polytope in whose vertices are all in . The volume of a lattice polytope P containing exactly k ≥ 1 points in d in its interior is bounded above by . Any lattice
On $\gamma$-vectors satisfying the Kruskal-Katona inequalities
We present examples of flag homology spheres whose $\gamma$-vectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter
Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials
Enriched p-partitions
An (ordinary) P -partition is an order-preserving map from a partially ordered set to a chain, with special rules specifying where equal values may occur. Examples include number-theoretic partitions
Facets and volume of Gorenstein Fano polytopes
It is known that every integral convex polytope is unimodularly equivalent to a face of some Gorenstein Fano polytope. It is then reasonable to ask whether every normal polytope is unimodularly
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