r-Stable hypersimplices.

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. [ABSTRACT FROM AUTHOR]