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 i > 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.