Stretched Schubert coefficients f_{u,v,w}(N) are eventually quasi-polynomial, proving Kirillov's conjecture that their generating function is rational.
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A boundary analogue of the Sturmfels correspondence equates the h*-polynomial of lattice-polytope boundaries with the h-polynomial of regular unimodular triangulations, yielding Dehn-Sommerville relations and symmetry/unimodality characterizations.
Preorder polytopes generalize arbor polytopes as lattice polytopes with a proven duality between Ehrhart polynomials and zeta polynomials of their lattice point posets, plus combinatorial volume interpretations and formulas for Ehrhart and h*-polynomials.
citing papers explorer
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Stretched Schubert coefficients are eventually quasi-polynomial
Stretched Schubert coefficients f_{u,v,w}(N) are eventually quasi-polynomial, proving Kirillov's conjecture that their generating function is rational.
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Boundary $h^\ast$-vectors and unimodular triangulations
A boundary analogue of the Sturmfels correspondence equates the h*-polynomial of lattice-polytope boundaries with the h-polynomial of regular unimodular triangulations, yielding Dehn-Sommerville relations and symmetry/unimodality characterizations.
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Polytopes and posets associated to preorders
Preorder polytopes generalize arbor polytopes as lattice polytopes with a proven duality between Ehrhart polynomials and zeta polynomials of their lattice point posets, plus combinatorial volume interpretations and formulas for Ehrhart and h*-polynomials.