The multisubset sum problem for finite abelian groups

2013/05/14 by Amela Muratovic-Ribic, Qiang Wang, Muratovic-Ribic, Amela +1
Mathematics · #05A15 #11B30 #11T06 #20K01 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A15 #msc:11B30 #msc:11T06 #msc:20K01

paper · pdf · doi:10.48550/arxiv.1305.3259

arxiv created 2013/05/14 · arxiv updated 2013/05/15

Abstract

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∈ 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.

Related

• On n-sum of an abelian group of order n
• On the number of subsequences with a given sum in a finite abelian group
• Open problems about sumsets in finite abelian groups: minimum sizes and critical numbers
• Sumsets with a minimum number of distinct terms
• Iterated Sumsets and Setpartitions