Applications of the Multisubset Sum Problem Over Finite Abelian Groups

In the article, we use the subset sum formula over a finite abelian group on the product of finite groups to derive the number of restricted partitions of elements in the group and to count the number of compositions over finite abelian groups. Later, we apply the formula for the multisubset sum problem on a group Zₙ to produce a new technique for studying restricted partitions of positive integers. 2020 Mathematics Subject Classification. 05A17, 11P81