Pattern-avoiding inversion sequences and open partition diagrams

By using the generating tree technique and the obstinate kernel method, Kim and Lin confirmed a conjecture due to Martinez and Savage which asserts that inversion sequences e = (e(1), e(2), ..., e(n)) containing no three indices i < j < k such that e(i) >= e(j), e(j) >= e(k) and e(j) >= e(k) are counted by Baxter numbers. In this paper, we provide a bijective proof of this conjecture via an intermediate structure of open partition diagrams, in answer to a problem posed by Beaton-Bouvel-Guerrini-Rinaldi. Moreover, we show that two new classes of pattern-avoiding inversion sequences are also counted by Baxter numbers. (C) 2020 Elsevier B.V. All rights reserved.