## SFU Discrete Math Seminar: Samantha Dahlberg

- Date: 11/15/2016

Simon Fraser University

Pattern Avoidance in Restricted Growth Functions

Wachs and White introduced four statistics on restricted growth functions or RGFs. An RGF is a sequence of positive integers $w=w_1w_2\dots w_n$ such that $w_1=1$ and $w_i \leq 1+\maw_1w_2\dots w_{i-1})$. We say that an RGF $w$ avoids $v$ if there is no subword of $w$ which standardizes to $v$ where standardize means we replace the $i$th smallest letter with $i$. Some of Wachs and Whites statistics are equidistubuted between different avoidance classes and even with different statistics on other combinatorial objects. We will particularly be showing that some of Wachs and White's statistics over the avoidance classes of $1212$ and $1221$ are equidistrubted with the area of two-colored Motzkin paths. These sets are related to non-crossing and non-nesting partitions. This is joint work with Robert Dorward, Jonathan Gerhard, Thomas Grubb, Carlin Purcell, Lindsey Campbell, and Bruce Sagan