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On dynamic algorithms for factorization invariants in numerical monoids


Authors: Thomas Barron, Christopher O’Neill and Roberto Pelayo
Journal: Math. Comp. 86 (2017), 2429-2447
MSC (2010): Primary 05C70, 11Y11
DOI: https://doi.org/10.1090/mcom/3160
Published electronically: December 27, 2016
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Abstract: Studying the factorization theory of numerical monoids relies on understanding several important factorization invariants, including length sets, delta sets, and $ \omega $-primality. While progress in this field has been accelerated by the use of computer algebra systems, many existing algorithms are computationally infeasible for numerical monoids with several irreducible elements. In this paper, we present dynamic algorithms for the factorization set, length set, delta set, and $ \omega $-primality in numerical monoids and demonstrate that these algorithms give significant improvements in runtime and memory usage. In describing our dynamic approach to computing $ \omega $-primality, we extend the usual definition of this invariant to the quotient group of the monoid and show that several useful results naturally extend to this broader setting.


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Additional Information

Thomas Barron
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: thomas.barron@uky.edu

Christopher O’Neill
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Address at time of publication: Department of Mathematics, University of California Davis, One Shields Avenue, Davis, California 95616
Email: coneill@math.ucdavis.edu

Roberto Pelayo
Affiliation: Department of Mathematics, University of Hawai‘i at Hilo, Hilo, Hawaii 96720
Email: robertop@hawaii.edu

DOI: https://doi.org/10.1090/mcom/3160
Received by editor(s): July 28, 2015
Received by editor(s) in revised form: February 20, 2016, and March 15, 2016
Published electronically: December 27, 2016
Article copyright: © Copyright 2016 American Mathematical Society