2023/07/19 by Nakic, Anamari
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2307.09852
A (G,[k1,…,kt],λ) \it partitioned difference family (PDF) is a partition \cal B of an additive group G into sets (\it blocks) of sizes k1, …, kt, such that the list of differences of \cal B covers exactly λ times every non-zero element of G. It is called \it Hadamard (HPDF) if the order of G is 2λ. The study of HPDFs is motivated by the fact that each of them gives rise, recursively, to infinitely many other PDFs. Apart from the \it elementary HPDFs consisting of a Hadamard difference set and its complement, only one HPDF was known. In this article we present three new examples in several groups and we start a general investigation on the possible existence of HPDFs with assigned parameters by means of simple arguments.