Perfect Bricks of Every Size

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Aug 22, 2013
Accession Number
AD1021716

Entities

People

  • Kurt Herzinger
  • Trae Holcomb

Organizations

  • United States Air Force Academy

Tags

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.