A Survey on Bent Partitions

Since their introduction, many results on bent partitions appeared in various directions and in several papers. The objective of this survey is to provide an introduction to this relatively young topic and a comprehensive overview of the main results. We present the known constructions of bent partitions, including those derived from generalized semifield spreads, their modifications, and secondary construction methods. We summarize the relations to special classes of vectorial bent functions and connections with combinatorial objects such as partial difference sets, strongly regular graphs, amorphic association schemes, and LP-packings. The article concludes with a discussion of several open problems.