Arithmagons and geometrically invariant multiplicative integer partitions. (English) Zbl 1349.05288
Summary: 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.
MSC:
05C78 | Graph labelling (graceful graphs, bandwidth, etc.) |
05C30 | Enumeration in graph theory |
11P99 | Additive number theory; partitions |