102-avoiding inversion sequences

초록

A sequence $(e_1,e_2,\cdots ,e_n)$ is an inversion sequences if $0\le e_i<i$ for all $i=1,\dots ,n$. We say that an inversion sequences $e=(e_1,e_2,\cdots ,e_n)$ \emph{contains} the pattern $102$ if there exist some indices $i<j<k$ such that $e_j<e_i<e_k$. Otherwise, $e$ is said to \emph{avoid} the pattern $102$. In this talk, we will construct a correspondence between the set of 2-Schr\"{o}der paths without peaks and valleys ending with a diagonal step and the set of $102$-avoiding inversion sequences. This is the joint work with JiSun Huh, Sangwook Kim, and Seunghyun Seo.