Generating Trees for 0021-Avoiding Inversion Sequences and a Conjecture of Hong and Li
Toufik Mansour · Discrete Mathematics Letters · 2023
An inversion sequence of length n is a word e = e0 • • • en which satisfies, for each i ∈ [n] = {0, 1, . . ., n}, the inequality 0 ≤ ei ≤ 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].