Families of critical sets for the dihedral group

Abstract

In this paper two new families of critical sets are presented for the Latin square defined by the dihedral group. This group has order 2n and is generated by {α,β\αⁿ = β² = e, αβ = βα^-1}. Sittampalam and Keedwell produce a critical set for the dihedral group in [6] for which they are unable to determine minimality. The present paper expands on their results.