2019/06/17 by Juan S. Auli, Auli, Juan S., Sergi Elizalde +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1906.07365
openalex publication_date 2019/06/18 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Inversion sequences are integer sequences e=e1e2… en such that 0≤ ei<i>,=,≠\, we study inversion sequences e with no subindex i such that eiR1ei+1R2ei+2. By enumerating such inversion sequences according to their length, we obtain well-known quantities such as Catalan numbers, Fibonacci numbers and central polynomial numbers, relating inversion sequences to other combinatorial structures. We also classify consecutive patterns of relations into Wilf equivalence classes, according to the number of inversion sequences avoiding them, and into more restrictive classes that consider the positions of the occurrences of the patterns. As a byproduct of our techniques, we obtain a simple bijective proof of a result of Baxter--Shattuck and Kasraoui about Wilf-equivalence of vincular patterns, and we prove a conjecture of Martinez and Savage, as well as related enumeration formulas for inversion sequences satisfying certain unimodality conditions.</i>