math.CO — Combinatorics

Partitioning $\{1,\dots,n\}$ into parts of size at most three whose sums are powers of three

Contributed by Deep Bhattacharjee, Ushashi Bhattacharya

We prove unconditionally the conjecture of Gurvich and Naumova that for every $n\ge1$ the set $\{1,\dots,n\}$ can be partitioned into parts of at most three elements whose sums are powers of $3$. The partition is given by an explicit recursion.