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arXiv · 2505.05171

Pattern avoidance in revised ascent sequences

Robin D. P. Zhou
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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.

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Robin D. P. Zhou. 2025-05-08. Pattern avoidance in revised ascent sequences. https://arxiv.org/abs/2505.05171

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