A new perspective on positivity in (consecutive) permutation patterns

Natasha Blitvić; Mohammed Slim Kammoun; Einar Steingrimsson

A new perspective on positivity in (consecutive) permutation patterns

Natasha Blitvić, Mohammed Slim Kammoun, Einar Steingrimsson

Mathematics And Statistics

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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.

Original language	English
Number of pages	12
Publication status	Published - 21 Jul 2023
Event	Formal Power Series and Algebraic Combinatorics 2023 - UC Davis, California, Davis, United States Duration: 17 Jul 2023 → 21 Jul 2023 http://fpsac23.math.ucdavis.edu/

Conference

Conference	Formal Power Series and Algebraic Combinatorics 2023
Abbreviated title	FPSAC
Country/Territory	United States
City	Davis
Period	17/07/23 → 21/07/23
Internet address	http://fpsac23.math.ucdavis.edu/

Keywords

permutation patterns
descent set
point processes
moment sequences

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Blitvi-etal-FPSAC-2023-Consecutive-ermutation-patterns-point-processes-and-moment-sequencesFinal published version, 170 KBLicence: Strath_1

Cite this

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T1 - A new perspective on positivity in (consecutive) permutation patterns

AU - Blitvić, Natasha

AU - Kammoun, Mohammed Slim

AU - Steingrimsson, Einar

PY - 2023/7/21

Y1 - 2023/7/21

N2 - 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.

AB - 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.

KW - permutation patterns

KW - descent set

KW - point processes

KW - moment sequences

M3 - Paper

T2 - Formal Power Series and Algebraic Combinatorics 2023

Y2 - 17 July 2023 through 21 July 2023

ER -

A new perspective on positivity in (consecutive) permutation patterns

Abstract

Conference

Keywords

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