Zenodo (CERN European Organization for Nuclear Research) · 2004 · 26 citations · 0 references
Natural SciencesComputer ScienceMathematicsNumber TheoryRepresentation TheorySet TheoryCombinatorial Set TheoryGenerating FunctionsInteger PartitionsPartition CoefficientPartition AlgebrasPartition FunctionPartition Generating FunctionsPartition IdentitiesRepresentation Functions
For a given set A of nonnegative integers the representation functions R<sub>2</sub>(A, n), R<sub>3</sub>(A, n) are defined as the number of solutions of the equation n = x+y, x, y ∈ A with condition x <y, x \leq y respectively. In this note we are going to determine the partitions of natural numbers into two parts such that their representation functions are the same from a certain point onwards.