Inversion sequences avoiding 021 and another pattern of length four

Toufik Mansour; Gökhan Yıldırım

doi:10.46298/DMTCS.10444

Inversion sequences avoiding 021 and another pattern of length four

Toufik Mansour, Gökhan Yıldırım

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the enumeration of inversion sequences that avoid pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of d-regular generating trees and conjecture that for any 021-avoiding pattern τ, the generating tree T ({021, τ}) is d-regular for some integer d.

Original language	English
Pages (from-to)	1-23
Number of pages	23
Journal	Discrete Mathematics and Theoretical Computer Science
Volume	252
DOIs	https://doi.org/10.46298/DMTCS.10444
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 by the author(s)

Keywords

Catalan numbers
Motzkin numbers
Pattern-avoiding inversion sequences
generating functions
generating trees
kernel method

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Discrete Mathematics and Combinatorics

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10.46298/DMTCS.10444

Cite this

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AB - We study the enumeration of inversion sequences that avoid pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of d-regular generating trees and conjecture that for any 021-avoiding pattern τ, the generating tree T ({021, τ}) is d-regular for some integer d.

KW - Catalan numbers

KW - Motzkin numbers

KW - Pattern-avoiding inversion sequences

KW - generating functions

KW - generating trees

KW - kernel method

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JO - Discrete Mathematics and Theoretical Computer Science

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ER -

Inversion sequences avoiding 021 and another pattern of length four

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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