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arXiv · 2512.01332

Counting Lattice Points in Generalized Permutohedra From A to B

Warut Thawinrak
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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.

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Warut Thawinrak. 2025-12-01. Counting Lattice Points in Generalized Permutohedra From A to B. https://arxiv.org/abs/2512.01332

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