Perfect Bricks of Every Size
Journal Article - Open Access
U.S. Air Force Academy Air Force Academy United States
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We answer an open question from a previous investigation related to numerical semigroups. For integers k, n greater or equal to 2 we prove the existence of a numerical semigroup S and a relative ideal I such that the size of the minimal generating set for I is k, the size of the minimal generating set for the dual, S-I, is n, and the size of the minimal generating for the ideal sum I S-I is nk.
- Statistics and Probability