Generalizing inplace multiplicity identities for integer compositions

Augustine O. Munagi, James Allen Sellers

Research output: Contribution to journalArticle

Abstract

In a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities. Since then, we asked whether one could generalize one of these results even further by considering compositions in which certain parts could come from t kinds (rather than just two kinds, which was the crux of the original result). In this paper, we provide such a generalization. A straightforward bijective proof is given and generating functions are provided for each of the types of compositions which arise. We close by briefly mentioning some arithmetic properties satisfied by the functions which count such compositions.

Original languageEnglish (US)
Pages (from-to)41-48
Number of pages8
JournalQuaestiones Mathematicae
Volume41
Issue number1
DOIs
StatePublished - Sep 16 2018

Fingerprint

Multiplicity
Integer
Integer Partitions
Bijective
Partition Function
Generating Function
Count
Partition
Generalise

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

Munagi, Augustine O. ; Sellers, James Allen. / Generalizing inplace multiplicity identities for integer compositions. In: Quaestiones Mathematicae. 2018 ; Vol. 41, No. 1. pp. 41-48.
@article{02653e131c4c405daba4c5c8dd688991,
title = "Generalizing inplace multiplicity identities for integer compositions",
abstract = "In a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities. Since then, we asked whether one could generalize one of these results even further by considering compositions in which certain parts could come from t kinds (rather than just two kinds, which was the crux of the original result). In this paper, we provide such a generalization. A straightforward bijective proof is given and generating functions are provided for each of the types of compositions which arise. We close by briefly mentioning some arithmetic properties satisfied by the functions which count such compositions.",
author = "Munagi, {Augustine O.} and Sellers, {James Allen}",
year = "2018",
month = "9",
day = "16",
doi = "10.2989/16073606.2017.1370030",
language = "English (US)",
volume = "41",
pages = "41--48",
journal = "Quaestiones Mathematicae",
issn = "1607-3606",
publisher = "Taylor and Francis Ltd.",
number = "1",

}

Generalizing inplace multiplicity identities for integer compositions. / Munagi, Augustine O.; Sellers, James Allen.

In: Quaestiones Mathematicae, Vol. 41, No. 1, 16.09.2018, p. 41-48.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Generalizing inplace multiplicity identities for integer compositions

AU - Munagi, Augustine O.

AU - Sellers, James Allen

PY - 2018/9/16

Y1 - 2018/9/16

N2 - In a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities. Since then, we asked whether one could generalize one of these results even further by considering compositions in which certain parts could come from t kinds (rather than just two kinds, which was the crux of the original result). In this paper, we provide such a generalization. A straightforward bijective proof is given and generating functions are provided for each of the types of compositions which arise. We close by briefly mentioning some arithmetic properties satisfied by the functions which count such compositions.

AB - In a recent paper, the authors gave two new identities for compositions, or ordered partitions, of integers. These identities were based on closely-related integer partition functions which have recently been studied. In the process, we also extensively generalized both of these identities. Since then, we asked whether one could generalize one of these results even further by considering compositions in which certain parts could come from t kinds (rather than just two kinds, which was the crux of the original result). In this paper, we provide such a generalization. A straightforward bijective proof is given and generating functions are provided for each of the types of compositions which arise. We close by briefly mentioning some arithmetic properties satisfied by the functions which count such compositions.

UR - http://www.scopus.com/inward/record.url?scp=85029529836&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029529836&partnerID=8YFLogxK

U2 - 10.2989/16073606.2017.1370030

DO - 10.2989/16073606.2017.1370030

M3 - Article

AN - SCOPUS:85029529836

VL - 41

SP - 41

EP - 48

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

SN - 1607-3606

IS - 1

ER -