English

Unimodality of a refinement of Lassalle's sequence

Combinatorics 2020-08-20 v1

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 \ell. They showed that each such sequence is symmetric in \ell and conjectured that these sequences are unimodal. We prove that the sequences are unimodal.

Keywords

Cite

@article{arxiv.2008.08222,
  title  = {Unimodality of a refinement of Lassalle's sequence},
  author = {Mihir Singhal},
  journal= {arXiv preprint arXiv:2008.08222},
  year   = {2020}
}