A central limit theorem for integer partitions into small powers

The study of the well-known partition function p(n) counting the number of solutions to n= a₁+ ⋯ + a_ℓ with integers 1 ≤ a₁≤ ⋯ ≤ a_ℓ has a long history in number theory and combinatorics. In this paper, we study a variant, namely partitions of integers into n=⌊a1α⌋+⋯+⌊aℓα⌋ with 1 ≤ a₁< ⋯ < a_ℓ and some fixed 0 < α< 1 . In particular, we prove a central limit theorem for the number of summands in such partitions, using the saddle-point method.