Year: 2026
Type: preprint
Abstract: We study three plane-partition enumerators arising from Schreier-Aigner's quasi-symmetry classes. Their realizations as lattice-point enumerators, together with staircase translations of interior lattice points, yield factorizations by Ehrhart-Macdonald reciprocity. We determine the consecutive linear factors, the parity and degree of the residual polynomials, and explicit divisibility bounds for their coefficient denominators. The denominator argument includes the half-integral translation required by the second-kind classes. We also derive a corrected size-five formula for the symmetric second-kind class. Exact computations verify irreducibility of the quasi-symmetric residual polynomials for every size from $3$ to $24$.
Source: arXiv (Cornell University)
Author: Cheng, Yinuo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213395959