## Combinatorics and Graph Theory

•  Quinn Minnich, Michigan State University
•  Counting Admissible Orderings of a Pinnacle Set
•  10/27/2021
•  3:00 PM - 3:50 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Bruce E Sagan (bsagan@msu.edu)

Let $S_n$ be the symmetric group. The pinnacle set of a permutation in $S_n$ is defined to be all elements of that permutation which are larger than both of their adjacent elements. Given a subset $P$ of $\{1,\ldots,n\}$ we can also ask if there exists a permutation in $S_n$ having $P$ as its pinnacle set. If so, we say $P$ is admissible. We can extend this idea further by ordering the elements of $P$ and asking if there exists a permutation in $S_n$ having pinnacle set $P$ with the elements of $P$ in the given order. If so, we say that the ordering is an admissible ordering. In this presentation, we will present an efficient recursion for counting the number of admissible orderings of a given pinnacle set.

## Contact

Department of Mathematics
Michigan State University