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

https://www.novapublishers.com/catalog/product_info.php?products_id=62614

Cite this

@article{34435b7be51b4c25930bc520a7f75cc1,

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",

year = "2017",

month = jan,

day = "1",

language = "American English",

volume = "9",

journal = "Journal of Combinatorics and Number Theory",

}

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

UR - https://www.novapublishers.com/catalog/product_info.php?products_id=62614

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

Other files and links

Fingerprint

Cite this