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FACTORIZATION LENGTH DISTRIBUTION FOR AFFINE SEMIGROUPS III: MODULAR EQUIDISTRIBUTION FOR NUMERICAL SEMIGROUPS WITH ARBITRARILY MANY GENERATORS

Part of: Algebraic combinatorics Semigroups

Published online by Cambridge University Press:  12 January 2021

STEPHAN RAMON GARCIA ,
MOHAMED OMAR ,
CHRISTOPHER O’NEILL  and
TIMOTHY WESLEY
STEPHAN RAMON GARCIA
Affiliation:
Department of Mathematics, Pomona College, 610 N. College Ave. Claremont, CA 91711, USA e-mail: stephan.garcia@pomona.edupages.pomona.edu/~sg064747
MOHAMED OMAR
Affiliation:
Department of Mathematics, Harvey Mudd College, 301 Platt Blvd. Claremont, CA 91711, USA e-mail: omar@g.hmc.eduwww.math.hmc.edu/~omar
CHRISTOPHER O’NEILL*
Affiliation:
Mathematics Department, San Diego State University, San Diego, CA 92182, USAcdoneill.sdsu.edu/
TIMOTHY WESLEY
Affiliation:
Department of Mathematics, Pomona College, 610 N. College Ave. Claremont, CA 91711, USA e-mail: tgwa2017@pomona.edu
*
e-mail: cdoneill@sdsu.edu
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Abstract

For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrary modulus. In particular, we prove that the factorization lengths are equidistributed across all congruence classes that are not trivially ruled out by modular considerations.

Keywords

factorizationnumerical semigroupquasipolynomial

MSC classification

Primary: 20M14: Commutative semigroups
Secondary: 05E40: Combinatorial aspects of commutative algebra
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 113 , Issue 1 , August 2022 , pp. 21 - 35
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by M. Giudici

The first author was partially supported by NSF grant DMS-1800123.

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