2025/12/15 by Hibi, Takayuki, Fakhari, Seyed Amin Seyed
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.12986
A lattice polytope P ⊂ ℝn of dimension n is called level* if (i) P is normal, (ii) (P ∖ ∂ P) ∩ ℤn ≠ ∅ and (iii) for each N = 2,3, … and for each a ∈ N(P ∖ ∂ P) ∩ ℤn, there is a0 ∈ (P ∖ ∂ P) ∩ ℤn together with a' ∈ (N-1)P ∩ ℤn for which a = a0 + a', where NP = \Na : a ∈ P\. A normal polytope P ⊂ ℝn of dimension n is called pseudo-Gorenstein* [4] if |(P ∖ ∂ P) ∩ ℤn| = 1. A pseudo-Gorenstein* polytope P is level* if and only if P is reflexive up to translation. In the present paper, level* polytopes together with pseudo-Gorenstein* polytopes arising from discrete polymatroids of bounded powers of edge ideals are studied.