Generating Trees for 0021-Avoiding Inversion Sequences and a Conjecture of Hong and Li

Abstract

An inversion sequence of length n is a word e = e 0 · · · e n which satisfies, for each i ∈ [ n ] = { 0 , 1 , . . . , n } , the inequality 0 ≤ e i ≤ i . In this paper, by generating tree tools, an explicit formula is found for the generating function for the number of inversion sequences of length n that avoid 0021 , which resolves the conjecture of Hong and Li posed in the recent paper [ Electron. J. Combin. 29 (2022) #4.37].