2025/07/23 by Toufik Mansour, Mansour, Toufik, Mark Shattuck +1
Computer Science · Engineering · #05A05 #05A15 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2507.17947
openalex publication_date 2025/07/23 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
Ascent sequences of length n avoiding the pattern 021 are enumerated by the n-th Catalan number Cn=(1)/(n+1)\binom2nn. In this paper, we extend this result and enumerate ascent sequences avoiding \021,τ\, where τ is a pattern of length four. We in turn identify all of the corresponding Wilf-equivalence classes and find generating function formulas corresponding to each class. In a couple of cases, we make use of an auxiliary statistic and the kernel method to ascertain the generating function. In several cases, our work of enumeration is shortened by establishing the equivalence of \021,τ\- and \021,τ'\-avoiders of a given length through an explicit bijection. As a consequence of our results, one obtains new combinatorial interpretations in terms of ascent sequences for several of the entries in the OEIS.