Arithmagons and Geometrically Invariant Multiplicative Integer Partitions

J. A. Franco, University of North Florida
J. Champion, Boise State University
J. W. Lyons, Nova Southeastern University


In this article, we introduce a formal definition for integral arithmagons. Informally, an integral arithmagon is a polygonal figure with integer labeled vertices and edges in which, under a binary operation, adjacent vertices equal the included edge. By considering the group of automorphisms for the associated graph, we count the number of integral arithmagons whose exterior sum or product equals a fixed number.