Universal conditions on h^*-vectors of lattice simplices

2018/12/25 by Higashitani, Akihiro · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Primary: 52B20 #Secondary: 52B12

paper · doi:10.48550/arxiv.1812.10123

Abstract

In this paper, we will prove that given a lattice simplex with its h^*-polynomial ∑_{i ≥ 0}h_i^*tⁱ, if h_k+1^*=⋯=h_2k^*=0 holds, then there exists a lattice simplex of degree k whose h^*-polynomial coincides with ∑_i=0^k h_i^*tⁱ. Moreover, we will present the examples showing that the condition h_k+1^*=h_k+2^*=⋯=h_2k-1^*=0 is necessary.

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• Smith Normal Forms of Graphical Hermite Simplices

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