Tuesday, September 24th, 2024
3:00 PM - 3:50 PM
Stratton Hall 205
Title:Near-Factorizations of Groups
Abstract: Let (G, ·) be a finite multiplicative group with identity e. For A, B ⊆ G, define AB = {gh : g ∈ A, h ∈ B}. We say that (A, B) is a near-factorization of G if |A| × |B| = |G| − 1 and G − e = AB. In this talk, we present various existence results for near-factorizations of cyclic and dihedral groups, including techniques for constructing and enumerating nonequivalent near-factorizations. We also discuss connections with other objects of combinatorial interest, including matrix factorizations, partitionable graphs, strong external difference families, and α-valuations (a type of graceful labelling) of graphs.
