对称约束构图
Symmetrically Constrained Compositions
摘要：
给定整数$a_1, a_2, ..., a_n$，用$a_1 + a_2 + ... + a_n \geq 1$，$M$到$n$非负部分的对称约束组合$λ_1 + lambda_2 + ... + lambda_n = M$是满足每个$n!$约束${\sum_{i=1}^n a_i λ_{π(i)} \geq 0 : π\in S_n}$的组合。我们将展示如何计算这些组合物的生成函数，结合从分区理论，排列统计，和格点枚举的方法。
英文摘要：
Given integers $a_1, a_2, ..., a_n$, with $a_1 + a_2 + ... + a_n \geq 1$, a symmetrically constrained composition $λ_1 + lambda_2 + ... + lambda_n = M$ of $M$ into $n$ nonnegative parts is one that satisfies each of the the $n!$ constraints ${\sum_{i=1}^n a_i λ_{π(i)} \geq 0 : π\in S_n}$. We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
