Andrews style partition identities

Andrews Style Partition Identities

We propose a method to construct a variety of partition identities at once. The main application is an all-moduli generalization of some of Andrews’ results in [5]. The novelty is that the method constructs solutions to functional equations which are satisfied by the generating functions. In contrast, the conventional approach is to show that a variant of well-known series satisfies the system ...

Proof of Andrews' Conjecture on Partition Identities

Bijective Proofs of Partition Identities of MacMahon, Andrews, and Subbarao

We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2, 3, 4, 6 (mod 6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.

Binomial Andrews-gordon-bressoud Identities

Binomial versions of the Andrews-Gordon-Bressoud identities are given.

Partition Identities

A partition of a positive integer n (or a partition of weight n) is a non-decreasing sequence λ = (λ1, λ2, . . . , λk) of non-negative integers λi such that ∑k i=1 λi = n. The λi’s are the parts of the partition λ. Integer partitions are of particular interest in combinatorics, partly because many profound questions concerning integer partitions, solved and unsolved, are easily stated, but not ...