Séminaire Lotharingien de Combinatoire, 89B.61 (2023), 12 pp.
Natasha Blitvić, Mohammed Slim Kammoun amd Einar Steingrímsson
A new Perspective on Positivity in (Consecutive) Permutation Patterns
Abstract.
We present a point of view on consecutive permutation patterns that interprets these in terms of (1) natural generalizations of the descent set of a permutation, (2) paths of a k-dependent point process, (3) refined clusters in the cluster method, and, surprisingly, (4) as conjectured moments of probability measures on the real line. At the heart of this paper is a recursive enumeration formula that allows us to get a grip on the aforementioned quantities and further enables us to formulate and numerically verify the conjecture (4), which provides a new unifying perspective on moment sequences arising from the study of permutation patterns.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
The following versions are available: