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Parts and Subword Patterns in Compositions
Journal of Combinatorics and Number Theory
  • Brian Hopkins, Saint Peter's University
  • Mark Shattuck, University of Tennessee
  • Andrew V. Sills, Georgia Southern University
  • Thotsaporn Thanatipanonda, Mahidol University International College
  • Hua Wang, Georgia Southern University
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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.

Citation Information
Brian Hopkins, Mark Shattuck, Andrew V. Sills, Thotsaporn Thanatipanonda, et al.. "Parts and Subword Patterns in Compositions" Journal of Combinatorics and Number Theory Vol. 9 Iss. 1 (2017) p. 1 - 14 ISSN: 1942-5600
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