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.
|Number of pages||40|
|Journal||Journal of Combinatorial Theory. Series A|
|State||Published - Jul 2018|
Bibliographical noteFunding 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).
© 2018 Elsevier Inc.
- Ehrhart h-vector
- r-stable hypersimplex
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics