发表机构
Capital Normal University（首都师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三个平面分拆计数函数，利用 Ehrhart-Macdonald 互反性实现因式分解，确定线性因子、剩余多项式性质及分母整除界，并验证小尺寸下的不可约性。
AI 中文摘要
我们研究了由 Schreier-Aigner 拟对称类产生的三个平面分拆计数函数。它们作为格点计数函数的实现，结合内部格点的阶梯平移，通过 Ehrhart-Macdonald 互反性得到因式分解。我们确定了连续线性因子、剩余多项式的奇偶性和次数，以及其系数分母的显式整除界。分母论证包括第二类类所需的半整数平移。我们还推导了对称第二类类的修正的五尺寸公式。精确计算验证了从 $3$ 到 $24$ 的所有尺寸下拟对称剩余多项式的不可约性。
英文摘要
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 $24$.
Comments18 pages
