PreprintCC BY 4.0arXiv
Ehrhart reciprocity and forced factors in three plane-partition enumerators
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 $24$.
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BibTeX
@misc{cheng2026ehrhart,
title = {{Ehrhart reciprocity and forced factors in three plane-partition enumerators}},
author = {Yinuo Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16765},
eprint = {2609.16765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16765},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ehrhart reciprocity and forced factors in three plane-partition enumerators
AU - Yinuo Cheng
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16765
UR - https://arxiv.org/abs/2609.16765
AB - 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 $24$.
ER -