2024/11/27 by Eon Lee, Andrés R. Vindas-Meléndez, Lee, Eon +3 · 1 voice
Mathematics · Engineering · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2411.18695
Building from the work of von Bell et al.~(2022), we study the Ehrhart theory of order polytopes arising from a special class of distributive lattices, known as generalized snake posets. We present arithmetic properties satisfied by the Ehrhart polynomials of order polytopes of generalized snake posets along with a computation of their Gorenstein index. Then we give a combinatorial description of the chain polynomial of generalized snake posets as a direction to obtain the h^*-polynomial of their associated order polytopes. Additionally, we present explicit formulae for the h^*-polynomial of the order polytopes of the two extremal examples of generalized snake posets, namely the ladder and regular snake poset. We then provide a recursive formula for the h^*-polynomial of any generalized snake posets and show that the h^*-vectors are entry-wise bounded by the h^*-vectors of the two extremal cases.