Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were ...

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with number ...

Let $p(n)$ denote the number of unrestricted partitions of $n$. The congruences referred to in the title are $p(5n + 4), p(7n + 5)$ and $p(11n + 6) \equiv 0$ (mod 5 ...

The year 2018 marks 100 years since the publication of one of the most startling results in the history of mathematics: Hardy and Ramanujan’s asymptotic formula for the partition function. To ...