Patterns and Parts in Compositions: Enumeration and Bijection

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

Patterns and Parts in Compositions: Enumeration and Bijection

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

Mathematical Sciences

Saint Peter's University
University of Tennessee, Knoxville
Mahidol University International College

Research output: Contribution to conference › Presentation

Abstract

A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with the empirical observation that, in the set of all compositions of n, the total number of odd parts equals the total number of runs. We explore proofs of this fact through combinatorial as well as generating function approaches. From there we show more general results relating the number of parts in a given residue class modulo m to various subword patterns among all compositions of n.

Original language	American English
State	Published - Oct 6 2016
Event	The Integers Conference - Duration: Oct 6 2016 → …

Conference

Conference	The Integers Conference
Period	10/6/16 → …

Disciplines

Mathematics
Physical Sciences and Mathematics

Keywords

Bijection
Compositions
Enumeration
Parts
Patterns

Cite this

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title = "Patterns and Parts in Compositions: Enumeration and Bijection",

abstract = " A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with the empirical observation that, in the set of all compositions of n, the total number of odd parts equals the total number of runs. We explore proofs of this fact through combinatorial as well as generating function approaches. From there we show more general results relating the number of parts in a given residue class modulo m to various subword patterns among all compositions of n.",

keywords = "Bijection, Compositions, Enumeration, Parts, Patterns",

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

year = "2016",

month = oct,

day = "6",

language = "American English",

note = "The Integers Conference ; Conference date: 06-10-2016",

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TY - CONF

T1 - Patterns and Parts in Compositions: Enumeration and Bijection

AU - Wang, Hua

AU - Hopkins, Brian

AU - Shattuck, Mark

AU - Sills, Andrew V.

AU - Thanatipanonda, Thotsaporn

PY - 2016/10/6

Y1 - 2016/10/6

N2 - A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with the empirical observation that, in the set of all compositions of n, the total number of odd parts equals the total number of runs. We explore proofs of this fact through combinatorial as well as generating function approaches. From there we show more general results relating the number of parts in a given residue class modulo m to various subword patterns among all compositions of n.

AB - A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with the empirical observation that, in the set of all compositions of n, the total number of odd parts equals the total number of runs. We explore proofs of this fact through combinatorial as well as generating function approaches. From there we show more general results relating the number of parts in a given residue class modulo m to various subword patterns among all compositions of n.

KW - Bijection

KW - Compositions

KW - Enumeration

KW - Parts

KW - Patterns

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpres/482

M3 - Presentation

T2 - The Integers Conference

Y2 - 6 October 2016

ER -

Patterns and Parts in Compositions: Enumeration and Bijection

Abstract

Conference

Disciplines

Keywords

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