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

Copyright

This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.