Injectivity of symmetric polynomial maps on partitions

Le résumé fourni par la source

Introduced by Ballantine, Beck, and Merca, the elementary symmetric partition function pre k , defined on the set of partitions with at least k parts, has been a topic of recent interest.We prove that pre k is injective on the set of m-ary partitions for positive integers m ≥ k, generalizing a k = 2 result of Ballantine, Beck, Merca, and Sagan, and complementing a result of Hadelyn, Niergarth, Weiyou Li, and Wenhui Li showing that, for each k ≥ 3, pre k is not injective on partitions of n with length 2k for infinitely many n.We introduce the skew Schur partition function prs λ ′ /µ ′ , prove injectivity results for particular choices of λ ′ , µ ′ , and describe an application to representation theory.

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