Congruences Involving F-Partition Functions

James Sellers

doi:10.1155/S0161171294000256

Congruences Involving F-Partition Functions

James Sellers

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

16 Scopus citations

Abstract

The primary goal of this note is to prove the congruence ϕ₃ (3n + 2) = 0 (mod 3), where ϕ₃ (n) denotes the number of F-partitions of n with at most F repetitions. Secondarily, we conjecture a new family of congruences involving cϕ₂ (n), the number of F-partitions of n with 2 colors.

Original language	English (US)
Pages (from-to)	187-188
Number of pages	2
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	17
Issue number	1
DOIs	https://doi.org/10.1155/S0161171294000256
State	Published - 1994
Externally published	Yes

Keywords

Congruence
partitions

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10.1155/S0161171294000256

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title = "Congruences Involving F-Partition Functions",

abstract = "The primary goal of this note is to prove the congruence ϕ3 (3n + 2) = 0 (mod 3), where ϕ3 (n) denotes the number of F-partitions of n with at most F repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2 (n), the number of F-partitions of n with 2 colors.",

keywords = "Congruence, partitions",

author = "James Sellers",

year = "1994",

doi = "10.1155/S0161171294000256",

language = "English (US)",

volume = "17",

pages = "187--188",

journal = "International Journal of Mathematics and Mathematical Sciences",

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TY - JOUR

T1 - Congruences Involving F-Partition Functions

AU - Sellers, James

PY - 1994

Y1 - 1994

N2 - The primary goal of this note is to prove the congruence ϕ3 (3n + 2) = 0 (mod 3), where ϕ3 (n) denotes the number of F-partitions of n with at most F repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2 (n), the number of F-partitions of n with 2 colors.

AB - The primary goal of this note is to prove the congruence ϕ3 (3n + 2) = 0 (mod 3), where ϕ3 (n) denotes the number of F-partitions of n with at most F repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2 (n), the number of F-partitions of n with 2 colors.

KW - Congruence

KW - partitions

UR - https://www.scopus.com/pages/publications/17844411251

UR - https://www.scopus.com/inward/citedby.url?scp=17844411251&partnerID=8YFLogxK

U2 - 10.1155/S0161171294000256

DO - 10.1155/S0161171294000256

M3 - Article

AN - SCOPUS:17844411251

SN - 0161-1712

VL - 17

SP - 187

EP - 188

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 1

ER -

Congruences Involving F-Partition Functions

Abstract

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