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Maximal factorization length for affine semigroups in dimension 2
Ponomarenko, VadimWhitney, Roger
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.
Mathematics and Statistics
San Diego State University
Master of Arts (M.A.) San Diego State University, 2020
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