Patterns and Parts in Compositions: Enumeration and Bijection

Presenters/Authors

Hua Wang, Georgia Southern UniversityFollow
Brian Hopkins, Saint Peter's UniversityFollow
Mark Shattuck, University of Tennessee
Andrew V. Sills, Georgia Southern UniversityFollow
Thotsaporn Thanatipanonda, Mahidol University International CollegeFollow

Document Type

Presentation

Presentation Date

10-6-2016

Abstract or Description

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 patterns among all compositions of n.

Sponsorship/Conference/Institution

The Integers Conference

Location

Carrolton, GA

Recommended Citation

Wang, Hua, Brian Hopkins, Mark Shattuck, Andrew V. Sills, Thotsaporn Thanatipanonda. 2016. "Patterns and Parts in Compositions: Enumeration and Bijection." Department of Mathematical Sciences Faculty Presentations. Presentation 482.
https://digitalcommons.georgiasouthern.edu/math-sci-facpres/482