The restricted binary partition function bk(n) enumerates the number of ways to represent n as n = 2a0 + 2a1 + ⋯ + 2aj with 0 ≤ a0 ≤ a1 ≤ ⋯ ≤ aj < k. We study the question of how large a power of 2 divides the difference bk(2r+2n)-bk-2(2rn) for fixed k ≥ 3, r ≥ 1, and all n ≥ 1.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics