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

University of Haifa

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	American English
Pages (from-to)	1-23
Number of pages	23
Journal	DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
Volume	252
Issue number	2
DOIs	https://doi.org/10.46298/DMTCS.10444
State	Published - 2023

Keywords

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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science
Discrete Mathematics and Combinatorics

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10.46298/DMTCS.10444

Cite this

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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.",

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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.

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KW - Motzkin numbers

KW - Pattern-avoiding inversion sequences

KW - generating functions

KW - generating trees

KW - kernel method

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Inversion sequences avoiding 021 and another pattern of length four

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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