Constructing 2 × 2 Bricks from Unitary Numerical Semigroups

Abstract

This paper investigates numerical semigroups that yield 2 × 2 bricks. We demonstrate the existence of an infinite family of 2 × 2 bricks that includes all of the perfect 2 × 2 bricks. We provide a formula for the Frobenius numbers of these semigroups as well as a necessary and sufficient condition for the semigroups to be symmetric.

Key Words:

• Dual
• Minimal generating set
• Monomial domain
• Numerical semigroup
• Relative ideal
• Tensor product
• Torsion
• Unitary

2010 Mathematics Subject Classification:

• 20M14

Notes

Communicated by I. Swanson.

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