Maximal factorization length for affine semigroups in dimension 2

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Title: Maximal factorization length for affine semigroups in dimension 2
Author(s): Grooms, Erin
Advisor(s): O'Neill, Chris
Committee Member(s): Ponomarenko, Vadim
Whitney, Roger
Date: 2020-08-06
Semester: Summer 2020
Type: Thesis
Extent: 41 pages
Abstract: An affine semigroup is a finitely generated subset closed under addition of Z d≥0. For each element a in the semigroup S, a factorization is a non-negative integer combination of the generators of S and the factorization length is the number of generators appearing in the sum. The present work generalizes previous results on maximal factorization length of numerical semigroups (affine semigroups of Z≥0) to higher dimensional affine semigroups. In this paper, we classify the asymptotic behavior of the maximal factorization length function for affine semigroups in dimension 2 with three or four generators, as well as discussing possible extensions to all affine semigroups dimension 2.
Language: en_US
Discipline: Mathematics
Department: Mathematics and Statistics
College: Sciences
Institution: San Diego State University
Degree: Master of Arts (M.A.) San Diego State University, 2020
Identifier: http://hdl.handle.net/20.500.11929/sdsu:109759