2025/02/14 by Yan Wang, Fang Qi, Wang, Yan +7
Computer Science · #05A05 #05A15 #05A19 #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2502.10128
openalex publication_date 2025/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by a correlation between the distribution of descents over permutations that avoid a consecutive pattern and those avoiding the respective quasi-consecutive pattern, as established in this paper, we obtain a complete \des-Wilf classification for quasi-consecutive patterns of length up to 4. For equivalence classes containing more than one pattern, we construct various descent-preserving bijections to establish the equivalences, which lead to the provision of proper versions of two incomplete bijective arguments previously published in the literature. Additionally, for two singleton classes, we derive explicit bivariate generating functions using the generalized run theorem.