Ehrhart Polynomials of Integral Simplices With Prime Volumes

2011/07/25 by Akihiro Higashitani, Higashitani, Akihiro · 1 citation
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Primary:52B20 Secondary:52B12 #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1107.4862

openalex publication_date 2011/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an integral convex polytope \Pc ⊂ \RR^N of dimension d, we call δ(\Pc)=(δ₀, δ₁,..., δ_d) the δ-vector of \Pc and \vol(\Pc)=∑_i=0^dδ_i its normalized volume. In this paper, we will establish the new equalities and inequalities on δ-vectors for integral simplices whose normalized volumes are prime. Moreover, by using those, we will classify all the possible δ-vectors of integral simplices with normalized volume 5 and 7.

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