THE NUMBER OF PARTS IN A RANDOM <i>t</i> -REGULAR PARTITION

Abstract For any integer $t \geq 2$ , we prove a local limit theorem (LLT) with an explicit convergence rate for the number of parts in a uniformly chosen t -regular partition. When $t = 2$ , this recovers the LLT for partitions into distinct parts, as previously established in the work of Szekeres [‘Asymptotic distributions of the number and size of parts in unequal partitions’, Bull. Aust. Math. Soc. 36 (1987), 89–97].