Applications of the Multisubset Sum Problem Over Finite Abelian Groups
DOI:
https://doi.org/10.5644/SJM.20.01.09Keywords:
partitions of integers, subset sum problem, multisubset sum problemAbstract
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 $\mathbb{Z}_n$ to produce a new technique for studying restricted partitions of positive integers.
2020 Mathematics Subject Classification. 05A17, 11P81
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References
Andrews, George E., The Theory of Partitions, Cambridge University Press, 1976.
G.H. Hardy, E.M. Wright An Introduction to the Theory of Numbers, Oxford at the Clerendon Press, 4th edition United Kingdom, 1960.
M. Kosters, The subset problem for finite abelian groups, J. Combin. Thery Ser. A 120(2013), 527-530.
Li and D. Wan, Counting subset sums of finite abelian groups, J. Combin. Thery Ser. A 199 (2012), no. 1, 170-182.
Amela Muratović-Ribić, Qiang Wang, The multisubset sum problem for finite abelian groups, Ars Mathematica Contemporanea 8 (2015), 417-423.
