On the Möbius functions and Frobenius constants of semigroups generated by linear forms of a special form. (Russian) Zbl 0675.20053

Koganov, L. M.

Semigroups and partial groupoids, Interuniv. Collect. Sci. Works, 15-25 (1987).

[For the entire collection see Zbl 0669.00006.]
The paper gives a method for obtaining the Möbius constant and the Möbius function for a semigroup with more than two generators, in some particular cases. Some known semigroups are considered, as well as the semigroup generated by the form \(xbc+yac+zab\), where a,b,c are relatively prime natural numbers or the semigroup generated by the form \(ax+by\), where a,b are relatively prime natural numbers different from 1.

Reviewer: M.Ştefănescu

MSC:

20M15	Mappings of semigroups
11A25	Arithmetic functions; related numbers; inversion formulas
20M05	Free semigroups, generators and relations, word problems

Keywords:

linear forms; Möbius constant; Möbius function; generators; semigroups