Congruence relations for r-colored partitions

Recurrences for 2-colored and 3-colored F-partitions

The goal of this paper is to prove new recurrences involving 2–colored and 3–colored generalized Frobenius partitions of n similar to the classical recurrence for the partition function p(n). Section

Asymptotic Relations for Partitions

Asymptotic relations are obtained for the number PA(n) of partitions of the integer n into summands from a set A of integers. The set A is subject to certain conditions; however the only arithmetic condition is that A have property Pk of Bateman and Erdös. A conjecture of Bateman and Erdös concerning the *th differences of p^(n) may be verified using these asymptotic relations. 1. Let A = {a0, ...

Labeled partitions with colored permutations

In this paper, we extend the notion of labeled partitions with ordinary permutations to colored permutations in the sense that the colors are endowed with a cyclic structure. We use labeled partitions with colored permutations to derive the generating function of the fmajk indices of colored permutations. The second result is a combinatorial treatment of a relation on the q-derangement numbers ...

Congruence Relations on Multilattices

Extending Congruence Relations

If 91 and 23 are algebras, where 9Is23, and 6 is a congruence relation on 91, let 0® be the smallest congruence relation on 93 containing 0. 91 is called a congruence subalgebra of 93 if 9ls93 and, for every congruence relation 0 on 91, 0*n|9I|2=0. Elementary subalgebras are congruence subalgebras, and there are Directed Union and Loewenheim-Skolem Theorems for congruence subalgebras analogous ...