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Pattern avoidance in revised ascent sequences

Combinatorics 2025-05-09 v1

Abstract

Inspired by the definition of modified ascent sequences, we introduce a new class of integer sequences called revised ascent sequences. These sequences are defined as Cayley permutations where each entry is a leftmost occurrence if and only if it serves as an ascent bottom. We construct a bijection between ascent sequences and revised ascent sequences by adapting the classic hat map, which transforms ascent sequences into modified ascent sequences. Additionally, we investigate revised ascent sequences that avoid a single pattern, leading to a wealth of enumerative results. Our main techniques include the use of bijections, generating trees, generating functions, and the kernel method.

Keywords

Cite

@article{arxiv.2505.05171,
  title  = {Pattern avoidance in revised ascent sequences},
  author = {Robin D. P. Zhou},
  journal= {arXiv preprint arXiv:2505.05171},
  year   = {2025}
}

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25 pages