Perfect Bricks of Every Size

reportActive / Technical Report | Accession Number: AD1021716 | Open PDF

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.

Author(s):
Herzinger, Kurt ; Holcomb, Trae
Author Organization(s):
U.S. Air Force Academy Air Force Academy United States
Descriptive Note:
Journal Article - Open Access
Supplementary Note:
Semigroup Forum Journal , 88, 1, 01 Jan 0001, 01 Jan 0001,
Pagination:
0021

Security Markings

DOCUMENT & CONTEXTUAL SUMMARY

Distribution:
Approved For Public Release
Distribution Statement:
Approved For Public Release;

RECORD

Collection: TR
Subject Terms
Communities of Interest:
No COI(s) Identified
Descriptor(s):
NUMERICAL ANALYSIS, INTEGER PROGRAMMING
Field(s)/Group(s):
Statistics and Probability
Keyword(s):
numerical semigroup, relative ideal, dual, minimal generating set
Report Date:
2013 Aug 22
Creation Date:
2013 Aug 22