Geodesic
The multisubset sum problem for finite abelian groups
Ars Mathematica Contemporanea, Tome 8 (2015) no. 2, pp. 417-423.

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We use a similar techique as in M. Kosters, The subset problem for finite abelian groups, J. Combin. Theory Ser. A 120 (2013), 527-530, to derive a formula for the number of multisubsets of a finite abelian group G with any given size and any given multiplicity such that the sum is equal to a given element g from G. This also gives the number of partitions of g into a given number of parts over a finite abelian group.
DOI : 10.26493/1855-3974.566.0da
Keywords: Composition, partition, subset sum, polynomials, finite fields, character, finite abelian groups. 
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Amela Muratović-Ribić; Qiang Wang. The multisubset sum problem for finite abelian groups. Ars Mathematica Contemporanea, Tome 8 (2015) no. 2, pp. 417-423. doi : 10.26493/1855-3974.566.0da. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.566.0da/

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