INVERSION SEQUENCES AVOIDING A SET OF LENGTH-3 PATTERNS

Toufik Mansour

doi:10.5281/zenodo.13768769

INVERSION SEQUENCES AVOIDING A SET OF LENGTH-3 PATTERNS

Toufik Mansour

Department of Mathematics

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

Abstract

An inversion sequence of size n is a sequence of integers e = e₀ · · · e_n such that 0 ≤ ei ≤ i, for all i = 0, 1,..., n. For a set of patterns B, let I_n(B) be the set of inversion sequences of length n that avoid all the patterns from B. We say that two sets of patterns B and C are I-Wilf-equivalent if |I_n(B)| = |I_n(C)|, for all n ≥ 0. Let w_d be the number of distinct I-Wilf-equivalence classes of subsets of exactly d length-3 patterns. This paper aims to prove that w₅ = 219, w₆ = 167, w₇ = 105, w₈ = 61, w₉ = 35, w₁₀ = 21, w₁₁ = 10, w₁₂ = 4, and w₁₃ = 1.

Original language	English
Article number	#A76
Journal	Integers
Volume	24
DOIs	https://doi.org/10.5281/zenodo.13768769
State	Published - 2024

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© 2024, EMUNI University. All rights reserved.

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

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title = "INVERSION SEQUENCES AVOIDING A SET OF LENGTH-3 PATTERNS",

abstract = "An inversion sequence of size n is a sequence of integers e = e0 · · · en such that 0 ≤ ei ≤ i, for all i = 0, 1,..., n. For a set of patterns B, let In(B) be the set of inversion sequences of length n that avoid all the patterns from B. We say that two sets of patterns B and C are I-Wilf-equivalent if |In(B)| = |In(C)|, for all n ≥ 0. Let wd be the number of distinct I-Wilf-equivalence classes of subsets of exactly d length-3 patterns. This paper aims to prove that w5 = 219, w6 = 167, w7 = 105, w8 = 61, w9 = 35, w10 = 21, w11 = 10, w12 = 4, and w13 = 1.",

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journal = "Integers",

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AB - An inversion sequence of size n is a sequence of integers e = e0 · · · en such that 0 ≤ ei ≤ i, for all i = 0, 1,..., n. For a set of patterns B, let In(B) be the set of inversion sequences of length n that avoid all the patterns from B. We say that two sets of patterns B and C are I-Wilf-equivalent if |In(B)| = |In(C)|, for all n ≥ 0. Let wd be the number of distinct I-Wilf-equivalence classes of subsets of exactly d length-3 patterns. This paper aims to prove that w5 = 219, w6 = 167, w7 = 105, w8 = 61, w9 = 35, w10 = 21, w11 = 10, w12 = 4, and w13 = 1.

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M3 - Article

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SN - 1553-1732

VL - 24

JO - Integers

JF - Integers

M1 - #A76

ER -

INVERSION SEQUENCES AVOIDING A SET OF LENGTH-3 PATTERNS

Abstract

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