The Dehn–Sommerville relations and the Catalan matroid

DOI10.1090/proc/13554zbMath1369.52017arXiv1512.04513OpenAlexW2963015812MaRDI QIDQ5274760

Anastasia Chavez, Nicole Yamzon

Publication date: 6 July 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.04513

zbMATH Keywords

Dehn-Sommerville relations\( f\)-vectorCatalan matroid

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40)

Cites Work

• A comparison theorem for \(f\)-vectors of simplicial polytopes
• The \(g\)-theorem matrices are totally nonnegative
• Binomial determinants, paths, and hook length formulae
• The number of faces of a simplicial convex polytope
• A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
• The Catalan matroid
• Lattice path matroids: Enumerative aspects and Tutte polynomials
• The numbers of faces of simplicial polytopes
• Positroids and non-crossing partitions
• Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes
• The unimodality conjecture for convex polytopes
• Lectures on Polytopes
• The maximum numbers of faces of a convex polytope
• On the Vector Representations of Induced Matroids
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