We discuss a family of restricted m-ary partition functions bm,j(n), which is the number of m-ary partitions of n with at most i + j copies of the part mi allowed. We then use generating function dissections to prove the following family of congruences for k ≥ 2 and 1≤t≤m-k + 1: bm,m-1(mk+1n + mk+t-1 + mk+t-2 + ⋯ + mk) ≡ 0 (mod 2t-1k).
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics