Back to Search Start Over

Distributions of statistics on separable permutations.

Authors :
Chen, Joanna N.
Kitaev, Sergey
Zhang, Philip B.
Source :
Discrete Applied Mathematics. Oct2024, Vol. 355, p169-179. 11p.
Publication Year :
2024

Abstract

We derive functional equations for distributions of six classical statistics (ascents, descents, left-to-right maxima, right-to-left maxima, left-to-right minima, and right-to-left minima) on separable and irreducible separable permutations. The equations are used to find a third degree equation for joint distribution of ascents and descents on separable permutations that generalizes the respective known result for the descent distribution. Moreover, our general functional equations allow us to derive explicitly (joint) distribution of any subset of maxima and minima statistics on irreducible, reducible and all separable permutations. In particular, there are two equivalence classes of distributions of a pair of maxima or minima statistics. Finally, we present three unimodality conjectures about distributions of statistics on separable permutations. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0166218X
Volume :
355
Database :
Academic Search Index
Journal :
Discrete Applied Mathematics
Publication Type :
Academic Journal
Accession number :
177748337
Full Text :
https://doi.org/10.1016/j.dam.2024.05.004