ON THE NUMBER OF EQUIVALENCE CLASSES OF BI-PARTITIONS ARISING FROM THE COLOR CHANGE

Byungchan Kim

doi:10.4134/CKMS.c230214

ON THE NUMBER OF EQUIVALENCE CLASSES OF BI-PARTITIONS ARISING FROM THE COLOR CHANGE

Byungchan Kim

School of Natural Sciences

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

Abstract

We introduce a new class of bi-partition function c_k(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for c_k(n) involves the partial theta function and obtain the following congruences: (Formula presented) and (Formula presented).

Original language	English
Pages (from-to)	345-352
Number of pages	8
Journal	Communications of the Korean Mathematical Society
Volume	39
Issue number	2
DOIs	https://doi.org/10.4134/CKMS.c230214
State	Published - 2024

Keywords

bi-partition
Color change
congruence
partial theta function

Access to Document

10.4134/CKMS.c230214

Cite this

@article{04486fa9e17f44d493c3bbd5aa9c33f8,

title = "ON THE NUMBER OF EQUIVALENCE CLASSES OF BI-PARTITIONS ARISING FROM THE COLOR CHANGE",

abstract = "We introduce a new class of bi-partition function ck(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for ck(n) involves the partial theta function and obtain the following congruences: (Formula presented) and (Formula presented).",

keywords = "bi-partition, Color change, congruence, partial theta function",

author = "Byungchan Kim",

note = "Publisher Copyright: {\textcopyright} 2024 Korean Mathematical Society",

year = "2024",

doi = "10.4134/CKMS.c230214",

language = "English",

volume = "39",

pages = "345--352",

journal = "Communications of the Korean Mathematical Society",

issn = "1225-1763",

number = "2",

}

TY - JOUR

T1 - ON THE NUMBER OF EQUIVALENCE CLASSES OF BI-PARTITIONS ARISING FROM THE COLOR CHANGE

AU - Kim, Byungchan

PY - 2024

Y1 - 2024

N2 - We introduce a new class of bi-partition function ck(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for ck(n) involves the partial theta function and obtain the following congruences: (Formula presented) and (Formula presented).

AB - We introduce a new class of bi-partition function ck(n), which counts the number of bi-color partitions of n in which the second color only appears at the parts that are multiples of k. We consider two partitions to be the same if they can be obtained by switching the color of parts that are congruent to zero modulo k. We show that the generating function for ck(n) involves the partial theta function and obtain the following congruences: (Formula presented) and (Formula presented).

KW - bi-partition

KW - Color change

KW - congruence

KW - partial theta function

UR - https://www.scopus.com/pages/publications/85195641633

U2 - 10.4134/CKMS.c230214

DO - 10.4134/CKMS.c230214

M3 - Article

AN - SCOPUS:85195641633

SN - 1225-1763

VL - 39

SP - 345

EP - 352

JO - Communications of the Korean Mathematical Society

JF - Communications of the Korean Mathematical Society

IS - 2

ER -

ON THE NUMBER OF EQUIVALENCE CLASSES OF BI-PARTITIONS ARISING FROM THE COLOR CHANGE

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this