Parts and Subword Patterns in Compositions

Brian Hopkins; Mark Shattuck; Andrew V. Sills; Thotsaporn Thanatipanonda; Hua Wang

Parts and Subword Patterns in Compositions

Brian Hopkins
, Mark Shattuck
, Andrew V. Sills
, Thotsaporn Thanatipanonda
, Hua Wang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Journal of Combinatorics and Number Theory
Volume	9
State	Published - Jan 1 2017

Disciplines

Education
Mathematics

Keywords

Parts
Subword Patterns
Compositions

Access to Document

http://home.dimacs.rutgers.edu/~asills/Comps/HopkinsShattuckSillsThanatipanondaWang.pdf

Cite this

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title = "Parts and Subword Patterns in Compositions",

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.",

keywords = "Parts, Subword Patterns, Compositions",

author = "Brian Hopkins and Mark Shattuck and Sills, \{Andrew V.\} and Thotsaporn Thanatipanonda and Hua Wang",

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language = "American English",

volume = "9",

journal = "Journal of Combinatorics and Number Theory",

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TY - JOUR

T1 - Parts and Subword Patterns in Compositions

AU - Hopkins, Brian

AU - Shattuck, Mark

AU - Sills, Andrew V.

AU - Thanatipanonda, Thotsaporn

AU - Wang, Hua

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Parts

KW - Subword Patterns

KW - Compositions

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/661

M3 - Article

VL - 9

JO - Journal of Combinatorics and Number Theory

JF - Journal of Combinatorics and Number Theory

ER -

Parts and Subword Patterns in Compositions

Abstract

Disciplines

Keywords

Access to Document

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Cite this