Symmetric semigroups with three generators

I. S. Vorob'ev, A. V. Ustinov

Pacific National University, Khabarovsk, Russia

Abstract: In the theory of numerical semigroups the Frobenius problem of finding the largest integer that does not belong to the given semigroup plays an important role. The study of the Frobenius problem suggests distinguishing the class of symmetric semigroups, which have a quite simple structure. The main result in this work is an asymptotic formula describing the growth of the number of symmetric semigroups with three generators.
Bibliography: 18 titles.

Keywords: numerical semigroup, Frobenius problem.

UDC: 511.33+512.53

MSC: Primary 20M14; Secondary 11B13, 11D04, 11D45

Received: 15.04.2019 and 15.05.2019

DOI: 10.4213/sm9262

 English version: Sbornik: Mathematics, 2019, 210:12, 1690–1701

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