Séminaire Lotharingien de Combinatoire, 78B.52 (2017), 12 pp.

Dongsu Kim and Zhicong Lin

Refined Restricted Inversion Sequences

Abstract. Recently, the study of patterns in inversion sequences was initiated by Corteel-Martinez-Savage-Weselcouch and Mansour-Shattuck independently. Motivated by their works and a double Eulerian equidistribution due to Foata (1977), we investigate several classical statistics on restricted inversion sequences that are either known or conjectured to be enumerated by Catalan, Large Schröder, Euler and Baxter numbers. One of the two highlights of our results is an intriguing bijection between 021-avoiding inversion sequences and (2413,4213)-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. The other one is a refinement of a conjecture due to Martinez and Savage that the cardinality of In(>=,>=,>) is the n-th Baxter number, which is proved via the so-called obstinate kernel method developed by Bousquet-Mélou.

Received: November 14, 2016. Accepted: February 17, 2017. Final version: April 1, 2017.

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