Counting Lattice Points in Generalized Permutohedra From A to B
Combinatorics
2025-12-02 v1
Abstract
We derive a formula for the number of lattice points in type B generalized permutohedra, providing a concise alternative to the formula obtained recently by Eur, Fink, Larson, and Spink as a result from a study of delta-matroids. Our approach builds upon the existing framework and techniques introduced by Postnikov in his work on type A generalized permutohedra, a family of polytopes interconnected with many mathematical concepts such as matroids and Weyl groups. In particular, we express the number of lattice points in type B generalized permutohedra in terms of Postnikov's notion of G-draconian sequences, from which their Ehrhart polynomials and volume formula follow as consequences.
Cite
@article{arxiv.2512.01332,
title = {Counting Lattice Points in Generalized Permutohedra From A to B},
author = {Warut Thawinrak},
journal= {arXiv preprint arXiv:2512.01332},
year = {2025}
}