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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 **I**_{n}(>=,>=,>) 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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