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International Journal of Mathematics and Mathematical Sciences
Volume 17, Issue 1, Pages 187-188
http://dx.doi.org/10.1155/S0161171294000256

Congruences involving F-partition functions

Department of Science and Mathematics, Cedarville College, Cedarville 45314, OH, USA

Received 10 August 1992

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The primary goal of this note is to prove the congruence ϕ3(3n+2)0(mod3), where ϕ3(n) denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F-partitions of n with 2 colors.