Simultaneous core multipartitions

Abstract: We initiate the study of simultaneous core multipartitions, generalising simultaneous core partitions, which have been studied extensively in the recent literature. Given a multipartition datum (s|c), which consists of a non-negative integer s and an l-tuple c of integers, we introduce the notion of an (s|c)-core multipartition. Given an arbitrary set of multicore data, we give necessary and sufficient conditions for the corresponding set of simultaneous core multipartitions to be finite. We then study the special case of simultaneous core bipartitions, giving exact enumerative results in some special subcases.