Geodesic
Refined Restricted Inversion Sequences
Séminaire lotharingien de combinatoire, 78B (2017)

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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. 

@article{SLC_2017_78B_a51,
     author = {Dongsu Kim and Zhicong Lin},
     title = {Refined {Restricted} {Inversion} {Sequences}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a51/}
}
TY  - JOUR
AU  - Dongsu Kim
AU  - Zhicong Lin
TI  - Refined Restricted Inversion Sequences
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a51/
ID  - SLC_2017_78B_a51
ER  - 
%0 Journal Article
%A Dongsu Kim
%A Zhicong Lin
%T Refined Restricted Inversion Sequences
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a51/
%F SLC_2017_78B_a51
Dongsu Kim; Zhicong Lin. Refined Restricted Inversion Sequences. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a51/