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.
@article{10_37236_12075,
author = {Anders Claesson and Atli Fannar Frankl{\'\i}n and Einar Steingr{\'\i}msson},
title = {Permutations with few inversions},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/12075},
zbl = {1532.05002},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12075/}
}
TY - JOUR
AU - Anders Claesson
AU - Atli Fannar Franklín
AU - Einar Steingrímsson
TI - Permutations with few inversions
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12075/
DO - 10.37236/12075
ID - 10_37236_12075
ER -
%0 Journal Article
%A Anders Claesson
%A Atli Fannar Franklín
%A Einar Steingrímsson
%T Permutations with few inversions
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12075/
%R 10.37236/12075
%F 10_37236_12075
Anders Claesson; Atli Fannar Franklín; Einar Steingrímsson. Permutations with few inversions. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/12075
