Permutations with few inversions

Anders Claesson; Atli Fannar Franklín; Einar Steingrímsson

Permutations with few inversions

Combinatorics 2023-05-17 v1

Authors: Anders Claesson , Atli Fannar Franklín , Einar Steingrímsson

Abstract

A curious generating function $S_0(x)$ for permutations of $[n]$ with exactly $n$ inversions is presented. Moreover, $(xC(x))^iS_0(x)$ is shown to be the generating function for permutations of $[n]$ with exactly $n-i$ inversions, where $C(x)$ is the generating function for the Catalan numbers.

Cite

@article{arxiv.2305.09457,
  title  = {Permutations with few inversions},
  author = {Anders Claesson and Atli Fannar Franklín and Einar Steingrímsson},
  journal= {arXiv preprint arXiv:2305.09457},
  year   = {2023}
}

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