Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903738 | Journal of Combinatorial Theory, Series A | 2018 | 16 Pages |
Abstract
We introduce Lipschitz functions on a finite partially ordered set P and study the associated Lipschitz polytope L(P). The geometry of L(P) can be described in terms of descent-compatible permutations and permutation statistics that generalize descents and big ascents. For ranked posets, Lipschitz polytopes are centrally-symmetric and Gorenstein, which implies symmetry and unimodality of the statistics. Finally, we define (P,k)-hypersimplices as generalizations of classical hypersimplices and give combinatorial interpretations of their volumes and hâ-vectors.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Raman Sanyal, Christian Stump,