Factorization length distribution for affine semigroups II: Asymptotic behavior for numerical semigroups with arbitrarily many generators

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:178

Article

Garcia, Stephan Ramon¹  Omar, Mohamed²  O'Neill, Christopher³  Yih, Samuel⁴ 

[1] Pomona Coll, Dept Math, 610 N Coll Ave, Claremont, CA 91711 USA

[2] Harvey Mudd Coll, Dept Math, 301 Platt Blvd, Claremont, CA 91711 USA

[3] San Diego State Univ, Math Dept, San Diego, CA 92182 USA

[4] UCLA, Math Dept, Box 951555, Los Angeles, CA 90095 USA

关键词: Numerical semigroup;    Monoid;    Factorization;    Quasipolynomial;    Mean;    Median;    Symmetric function;    Homogeneous symmetric function;   

DOI  :  10.1016/j.jcta.2020.105358

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free