r-Stable hypersimplices

Benjamin Braun, Liam Solus

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Hypersimplices are well-studied objects in combinatorics, optimization, and representation theory. For each hypersimplex, we define a new family of subpolytopes, called r-stable hypersimplices, and show that a well-known regular unimodular triangulation of the hypersimplex restricts to a triangulation of each r-stable hypersimplex. For the case of the second hypersimplex defined by the two-element subsets of an n-set, we provide a shelling of this triangulation that sequentially shells each r-stable sub-hypersimplex. In this case, we utilize the shelling to compute the Ehrhart h-polynomials of these polytopes, and the hypersimplex, via independence polynomials of graphs. For one such r-stable hypersimplex, this computation yields a connection to CR mappings of Lens spaces via Ehrhart–MacDonald reciprocity.

Original languageEnglish
Pages (from-to)349-388
Number of pages40
JournalJournal of Combinatorial Theory. Series A
Volume157
DOIs
StatePublished - Jul 2018

Bibliographical note

Funding Information:
Benjamin Braun was partially supported by the National Security Agency through awards H98230-13-1-0240 and H98230-16-1-0045. Liam Solus was partially supported by a 2014 National Science Foundation/Japan Society for the Promotion of Science East Asia and Pacific Summer Institute Fellowship (EAPSI award 1414621).

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

  • Ehrhart h-vector
  • Hypersimplex
  • Shelling
  • Triangulation
  • Unimodal
  • r-stable hypersimplex

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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