Sets in Abelian Groups with Distinct Sums of Pairs

Reference:

Harri Haanpää and Patric R. J. Östergård. Sets in Abelian groups with distinct sums of pairs. Research Report A87, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Espoo, Finland, February 2004.

Abstract:

A subset ( S=left s_1,ldots ,s_kright ) of an Abelian group ( G ) is called an ( S_t )-set of size ( k ) if all sums of ( t ) different elements in ( S ) are distinct. Let denote the cardinality of the largest -set in . Let ( v! left( kright) ) denote the order of the smallest Abelian group for which . We develop bounds for , and we determine for by determining for Abelian groups of order up to using exhaustive backtrack search with isomorph rejection.

Keywords:

additive base, backtrack search, difference set, packing

Suggested BibTeX entry:

@techreport{HUT-TCS-A87,
    address = {Espoo, Finland},
    author = {Harri Haanp{\"a}{\"a} and Patric R. J. {\"O}sterg{\aa}rd},
    institution = {Helsinki University of Technology, Laboratory for Theoretical Computer Science},
    month = {February},
    number = {A87},
    pages = {10},
    title = {Sets in {A}belian Groups with Distinct Sums of Pairs},
    type = {Research Report},
    year = {2004},
}