Generating trees for 0021-avoiding inversion sequences and a conjecture of Hong and Li

Toufik Mansour

doi:10.47443/dml.2023.012

Generating trees for 0021-avoiding inversion sequences and a conjecture of Hong and Li

Toufik Mansour

Department of Mathematics

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

Abstract

An inversion sequence of length n is a word e = e₀ · · · e_n which satisfies, for each i ∈ [n] = {0, 1, …, n}, the inequality 0 ≤ e_i ≤ i. In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021, which resolves the conjecture of Hong and Li posed in the recent paper [Electron. J. Combin. 29 (2022) #4.37].

Original language	English
Pages (from-to)	11-14
Number of pages	4
Journal	Discrete Mathematics Letters
Volume	12
DOIs	https://doi.org/10.47443/dml.2023.012
State	Published - 2023

Bibliographical note

Publisher Copyright:
© 2023 the author.

Keywords

0021-avoiding inversion sequences
generating trees
inversion sequences

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.47443/dml.2023.012

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abstract = "An inversion sequence of length n is a word e = e0 · · · en which satisfies, for each i ∈ [n] = {0, 1, …, n}, the inequality 0 ≤ ei ≤ i. In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021, which resolves the conjecture of Hong and Li posed in the recent paper [Electron. J. Combin. 29 (2022) #4.37].",

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AB - An inversion sequence of length n is a word e = e0 · · · en which satisfies, for each i ∈ [n] = {0, 1, …, n}, the inequality 0 ≤ ei ≤ i. In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021, which resolves the conjecture of Hong and Li posed in the recent paper [Electron. J. Combin. 29 (2022) #4.37].

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KW - generating trees

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Generating trees for 0021-avoiding inversion sequences and a conjecture of Hong and Li

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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