Congruences for 2t-Core Partition Functions

Partition congruences by involutions

We present a general construction of involutions on integer partitions which enable us to prove a number of modulo 2 partition congruences. Introduction The theory of partitions is a beautiful subject introduced by Euler over 250 years ago and is still under intense development [2]. Arguably, a turning point in its history was the invention of the “constructive partition theory” symbolized by F...

Square - Partition Congruences

ARITHMETIC OF 3t-CORE PARTITION FUNCTIONS

Let t 1 be an integer and a3t(n) be the number of 3t-cores of n. We prove a class of congruences for a3t(n)mod 3 by Hecke nilpotence.

Congruences of the Partition Function

Ramanujan also conjectured that congruences (1) exist for the cases A = 5 , 7 , or 11 . This conjecture was proved by Watson [17] for the cases of powers of 5 and 7 and Atkin [3] for the cases of powers of 11. Since then, the problem of finding more examples of such congruences has attracted a great deal of attention. However, Ramanujan-type congruences appear to be very sparse. Prior to the la...

Ramanujan Type Congruences for a Partition Function

We investigate the arithmetic properties of a certain function b(n) given by ∞ ∑ n=0 b(n)qn = (q; q)−2 ∞ (q 2; q2)−2 ∞ . One of our main results is b(9n + 7) ≡ 0 (mod 9).