Congruences Involving F-Partition Functions

James Sellers

doi:10.1155/S0161171294000256

Congruences Involving F-Partition Functions

James Sellers

Mathematics

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

14 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

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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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.",

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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.

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JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

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Congruences Involving F-Partition Functions

Abstract

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