Unimodality of a refinement of Lassalle's sequence

preprint2020arXivOpen access

Abstract

Defant, Engen, and Miller defined a refinement of Lassalle's sequence Ak+1A_{k+1} by considering uniquely sorted permutations of length 2k+12k+1 whose first element is ℓ\ell. They showed that each such sequence is symmetric in ℓ\ell and conjectured that these sequences are unimodal. We prove that the sequences are unimodal.

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