Parts and Subword Patterns in Compositions

Authors

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

Document Type

Article

Publication Date

2017

Publication Title

Journal of Combinatorics and Number Theory

ISSN

1942-5600

Abstract

We find relationships between subword patterns and residue classes of parts in the set of integer compositions of a given weight. In particular, we show that it is always possible to express the total number of parts in compositions of n that are congruent to i modulo m as a linear combination of the total number of occurrences of subword patterns of length no more than m. We also find an explicit formula enumerating all such parts.

Recommended Citation

Hopkins, Brian, Mark Shattuck, Andrew V. Sills, Thotsaporn Thanatipanonda, Hua Wang. 2017. "Parts and Subword Patterns in Compositions." Journal of Combinatorics and Number Theory, 9 (1): 1-14.
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/661