2022/07/25 by Konan, Isaac
#05A17 (Primary) 11P83 #11B30 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2207.12366
For all positive integers k,l,n, the Little Glaisher theorem states that the number of partitions of n into parts not divisible by k and occurring less than l times is equal to the number of partitions of n into parts not divisible by l and occurring less than k times. While this refinement of Glaisher theorem is easy to establish by computation of the generating function, there is still no one-to-one canonical correspondence explaining it. Our paper brings an answer to this open problem through an arithmetical approach. Furthermore, in the case l=2, we discuss the possibility of constructing a Schur-type companion of the Little Glaisher theorem via the weighted words.