Amela Muratovic-Ribic, Qiang Wang
Published 2013-05-14Version 1
In this note, we give the explicit formula for the number of multisubsets of a finite abelian group $G$ with any given size such that the sum is equal to a given element $g\in G$. This also gives the number of partitions of $g$ into a given number of parts over a finite abelian group. An inclusion-exclusion formula for the number of multisubsets of a subset of $G$ with a given size and a given sum is also obtained.
An explicit formula for the number of permutations with a given number of alternating runs
On the number of partitions of $n$ whose product of the summands is at most $n$
An explicit formula for Bell numbers in terms of Stirling numbers and hypergeometric functions
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