A packing of partial difference sets is a collection of disjoint partial difference sets in a finite
group $ G $. This configuration has received considerable attention in design theory, finite …

There exist few examples of negative Latin square type partial difference sets (NLST PDSs)
in nonabelian groups. We present a list of 176 inequivalent NLST PDSs in 48 …

We introduce and explore near-complete external difference families, a partitioning of the
nonidentity elements of a group so that each nonidentity element is expressible as a …

A Hadamard matrix is balanced splittable if some subset of its rows has the property that the
dot product of every two distinct columns takes at most two values. This definition was …

A $(v, k,\lambda,\mu) $-partial difference set (PDS) is a subset $ D $ of a group $ G $ such
that $| G|= v $, $| D|= k $, and every nonidentity element $ x $ of $ G $ can be written in …

In this paper, we consider regular automorphism groups of graphs in the RT2 family and the
Davis‐Xiang family and amorphic abelian Cayley schemes from these graphs. We derive …

In this paper we construct several infinite families of partial difference sets of both the Latin
and negative Latin square type. Among these constructions is a new family having …

Cyclotomic association schemes of broad classes and applications to the construction of
combinatorial structures* Page 1 Accepted manuscript ISSN 2590-9770 The Art of Discrete and …

In this paper we prove non-existence of nontrivial partial difference sets in Abelian groups of
order 8 p^ 3 8 p 3, where p ≥ 3 p≥ 3 is a prime number. These groups seemed to have the …

In the study of (partial) difference sets and their generalizations in groups G, the most widely
used method is to translate their definition into an equation over group ring Z [G] and to …