Schroder paths without triple descents and $(101, 102)$-avoiding inversion sequences

초록

A Schr\"{o}der path is a lattice path from $(0,0)$ to $(2n,0)$ with steps $(1,1)$, $(1,-1)$ and $(2,0)$ that never goes below the $x$-axis. 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 $(101,102)$ if there exist some indices $i<j<k$ such that $e_j<e_i\le e_k$. Otherwise, $e$ is said to \emph{avoid} $p$. In this talk, we will construct a correspondence between the set of Schr\"{o}der paths without triple descents and the set of $(101,102)$-avoiding inversion sequences. This is the joint work with JiSun Huh, Sangwook Kim, and Seunghyun Seo.