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Factorization length distribution for affine semigroups. II: Asymptotic behavior for numerical semigroups with arbitrarily many generators. (English) Zbl 1477.20115

Authors’ abstract: For numerical semigroups with a specified list of (not necessarily minimal) generators, we obtain explicit asymptotic expressions, and in some cases quasipolynomial/quasirational representations, for all major factorization length statistics. This involves a variety of tools that are not standard in the subject, such as algebraic combinatorics (Schur polynomials), probability theory (weak convergence of measures, characteristic functions), and harmonic analysis (Fourier transforms of distributions). We provide instructive examples which demonstrate the power and generality of our techniques. We also highlight unexpected consequences in the theory of homogeneous symmetric functions.
For Part I see [S. R. Garcia et al., Eur. J. Comb. 78, 190–204 (2019; Zbl 1477.20116)].

MSC:

20M14 Commutative semigroups
20M13 Arithmetic theory of semigroups
11R27 Units and factorization
13A05 Divisibility and factorizations in commutative rings

Citations:

Zbl 1477.20116
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