We give a natural definition of rowmotion for $321$-avoiding permutations, by translating, through bijections involving Dyck paths and the Lalanne--Kreweras involution, the analogous notion for antichains of the positive root poset of type $A$. We prove that some permutation statistics, such as the number of fixed points, are homomesic under rowmotion, meaning that they have a constant average over its orbits. Our setting also provides a more natural description of the celebrated Armstrong--Stump--Thomas equivariant bijection between antichains and non-crossing matchings in types $A$ and $B$, by showing that it is equivalent to the Robinson--Schensted--Knuth correspondence on $321$-avoiding permutations permutations.
@article{10_37236_11792,
author = {Ben Adenbaum and Sergi Elizalde},
title = {Rowmotion on 321-avoiding permutations},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {3},
doi = {10.37236/11792},
zbl = {1519.05001},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11792/}
}
TY - JOUR
AU - Ben Adenbaum
AU - Sergi Elizalde
TI - Rowmotion on 321-avoiding permutations
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/11792/
DO - 10.37236/11792
ID - 10_37236_11792
ER -
%0 Journal Article
%A Ben Adenbaum
%A Sergi Elizalde
%T Rowmotion on 321-avoiding permutations
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/11792/
%R 10.37236/11792
%F 10_37236_11792
Ben Adenbaum; Sergi Elizalde. Rowmotion on 321-avoiding permutations. The electronic journal of combinatorics, Tome 30 (2023) no. 3. doi: 10.37236/11792
