## Integer compositions: subword patterns and parts

- Feb. 26, 2016
- 2:30 p.m.
- LeConte 312

## Abstract

A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with the empirical observation that in the set of all compositions of n, the total number of odd parts equals the total number of runs. We explore proofs of this fact through combinatorial as well as generating function approaches. From there we show more general results relating the number of parts in a given residue class modulo m to various subword patters among all compositions of n. This is joint work with Brian Hopkins, Drew Sills, and Thotsaporn Thanatipananonda.