Congruences for k-elongated plane partition diamonds

Plane Partition Diamonds and Generalizations

SYLVIE CORTEEL AND CARLA D. SAVAGE Abstra t. In this note we generalize the plane partition diamonds of Andrews, Paule, and Riese to plane partition polygons and plane tree diamonds and show how to ompute their generating fun tions. 1. Introdu tion In [1℄, Andrews, Paule, and Riese introdu e the family of plane partition diamonds. A plane partition diamond of length n is a sequen e of length 3n...

Infinite Families of Strange Partition Congruences for Broken 2-diamonds

In 2007 George E. Andrews and Peter Paule [1] introduced a new class of combinatorial objects called broken k-diamonds. Their generating functions connect to modular forms and give rise to a variety of partition congruences. In 2008 Song Heng Chan proved the first infinite family of congruences when k = 2. In this note we present two non-standard infinite families of broken 2-diamond congruence...

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

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...