Symmetrically constrained compositions
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Abstract
Given integers a 1,a 2,…,a n , with a 1+a 2+⋅⋅⋅+a n ≥1, a symmetrically constrained composition λ 1+λ 2+⋅⋅⋅+λ n =M of M into n nonnegative parts is one that satisfies each of the n! constraints \(\{\sum_{i=1}^{n}a_{i}\lambda_{\pi(i)}\geq 0:\pi \in S_{n}\}\). We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.
Keywords
Symmetrically constrained composition Partition analysis Permutation statistics Generating function Lattice-point enumerationMathematics Subject Classification (2000)
05A17 05A15 11P21Preview
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