2017/06/22 by Kim, Dongsu, Lin, Zhicong · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1706.07208
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 \em Catalan, \em Large Schröder, \em Baxter and \em Euler numbers. One of the two highlights of our results is a fascinating bijection between 000-avoiding inversion sequences and Simsun permutations, which together with Foata's V- and S-codes, provide a proof of a restriced double Eulerian equdistribution. 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 \em obstinate kernel method developed by Bousquet-Mélou.