Pairing conjugate partitions by residue classes

Pairing conjugate partitions by residue classes

We study integer partitions in which the parts fulfill the same congruence relations with the parts of their conjugates, called conjugate–congruent partitions. The results obtained include uniqueness criteria, weight lower-bounds and enumerating generating functions. © 2007 Elsevier B.V. All rights reserved. MSC: 11P81; 11P83; 05A15

Dominant residue classes concerning the summands of partitions

Classes of Independent Partitions

Let X, Y be sets and let R, S be relations between X and Y . Let us observe that R ⊆ S if and only if: (Def. 1) For every element x of X and for every element y of Y such that 〈x, y〉 ∈ R holds 〈x, y〉 ∈ S. For simplicity, we adopt the following rules: Y is a non empty set, a is an element of Boolean , G is a subset of PARTITIONS(Y ), and P , Q are partitions of Y . Let Y be a non empty set and l...

The Number of Parts in Certain Residue Classes of Integer Partitions

We use the Circle Method to derive asymptotics for functions related to the number of parts of partitions in particular residue classes.

On the Number of Parts of Integer Partitions Lying in given Residue Classes

Improving upon previous work [3] on the subject, we use Wright’s Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer n that are in any given arithmetic progression.