A numerical semigroup S is a set of nonnegative integers such that S contains 0, S is closed under addition, and the complement of S is finite. This paper considers pairs (S,I) of a given numerical semigroup S and corresponding relative ideal I such that \mu(I)\mu(S-I) = \mu(I+(S-I)), where \mu denotes the size of the minimal generating set and S-I is the dual of I in S. We will present recent results in the research of such pairs (perfect bricks) with \mu(I) > 2 and \mu(S-I) > 2. We will also show the existence of an infinite family of perfect bricks.
"Recent Developments in Perfect Bricks with Dimension Higher than 2 x 2,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 13
, Article 7.
Available at: https://scholar.rose-hulman.edu/rhumj/vol13/iss1/7