Volume 92, Number 2 (2000), in the article “The 2-Adic Behavior of the Number of Partitions into Distinct Parts,” by Ken Ono and David Penniston, pages 138–157 ()

The 2-Adic Behavior of the Number of Par

The 2-Adic Behavior of the Number of Partitions into Distinct Parts

✍ Ken Ono; David Penniston 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 171 KB

Let Q(n) denote the number of partitions of an integer n into distinct parts. For positive integers j, the first author and B. Gordon proved that Q(n) is a multiple of 2 j for every non-negative integer n outside a set with density zero. Here we show that if i 0 (mod 2 j ), then In particular, Q(n)