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Modified ascent sequences avoiding a pattern of length 4

Part of: Graph theory Combinatorics

Published online by Cambridge University Press:  07 August 2025

Zhicong Lin ,
Yongchun Zang  and
Dapao Zhou
Zhicong Lin
Affiliation:
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, PR China
Yongchun Zang
Affiliation:
College of Mathematics Physics and Information, Shaoxing University, Shaoxing, PR China
Dapao Zhou*
Affiliation:
College of Mathematics Physics and Information, Shaoxing University, Shaoxing, PR China
*
Corresponding author: Dapao Zhou, email: dapao2012@163.com
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Abstract

Modified ascent sequences, initially defined as the bijective images of ascent sequences under a certain hat map, have also been characterized as Cayley permutations where each entry is a leftmost copy if and only if it is an ascent top. These sequences play a significant role in the study of Fishburn structures. In this paper, we investigate (primitive) modified ascent sequences avoiding a pattern of length 4 by combining combinatorial and algebraic techniques, including the application of the kernel method. Our results confirm several conjectures posed by Cerbai.

Keywords

ascent sequencesmodified ascent sequencesCatalan numberspattern avoidancekernel method

MSC classification

Primary: 05A05: Permutations, words, matrices
Secondary: 05C30: Enumeration in graph theory

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , First View , pp. 1 - 29
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Edinburgh Mathematical Society.

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