On dynamic algorithms for factorization invariants in numerical monoids
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- by Thomas Barron, Christopher O’Neill and Roberto Pelayo PDF
- Math. Comp. 86 (2017), 2429-2447 Request permission
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.References
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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
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 86 (2017), 2429-2447
- MSC (2010): Primary 05C70, 11Y11
- DOI: https://doi.org/10.1090/mcom/3160
- MathSciNet review: 3647965