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The Diophantine Frobenius Problem$
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Jorge L. Ramírez Alfonsín

Print publication date: 2005

Print ISBN-13: 9780198568209

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568209.001.0001

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Numerical semigroups

Numerical semigroups

(p.135) 7 Numerical semigroups
The Diophantine Frobenius Problem

J. L. Ramírez Alfonsín

Oxford University Press

This chapter introduces the concept of numerical semigroups. Several properties of the gaps and nongaps of a semigroup are investigated, and the importance of the role played by the Frobenius number (also known as conductor) in the study of symmetric and pseudo-symmetric semigroups is pointed out. A number of results relating FP to telescopic semigroups, the famous Apéry Sets (used by R. Apéry in the study of algebroid planar branches), type sequences in semigroups, complete intersection semigroups, -hyperelliptic semigroups (motivated by the study of Weierstrass semigroups), the Möbius function, and other related concepts are proved.

Keywords:   semigroups, nongaps, symmetric-semigroups, gaps, Apéry Sets

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