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

Published online by Cambridge University Press:  12 January 2021

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

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.

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