Séminaire Lotharingien de Combinatoire, 78B.52 (2017), 12 pp.
Dongsu Kim and Zhicong Lin
Refined Restricted Inversion Sequences
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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