2004/10/07 by Christos A. Athanasiadis · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Advanced Mathematical Identities #Polytope #Mathematics #Combinatorics #Lattice (music) #Order (exchange) #Dimension (graph theory) #Semigroup #Discrete mathematics
paper · pdf · doi:10.37236/1863
openalex publication_date 2004/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Conditions are given on a lattice polytope P of dimension m or its associated affine semigroup ring which imply inequalities for the h^*-vector (h^*0, h^*1,…,h^*m) of P of the form h^*i ≥ h^*d-i for 1 ≤ i ≤ \lfloor d / 2 \rfloor and h^*\lfloor d / 2 \rfloor ≥ h^*\lfloor d / 2 \rfloor + 1 ≥ ⋯ ≥ h^*d, where h^*i = 0 for d < i ≤ m. Two applications to order polytopes of posets and stable polytopes of perfect graphs are included.