×
Chapman, S. T.; García-Sánchez, P. A.; Llena, D.

The catenary and tame degree of numerical monoids. (English) Zbl 1177.20070

Forum Math. 21, No. 1, 117-129 (2009).
The authors construct an algorithm for computing the catenary and tame degrees of numerical monoids, i.e., submonoids of nonnegative integers under addition with finite complement. A numerical monoid \(S\) has a finite minimal generating set \(\{n_1,\dots,n_p\}\). A factorization of an element \(n\) in \(S\) is a \(p\)-tuple \((a_1,\dots,a_p)\) such that \(n=a_1n_1+\cdots+a_pn_p\). Such factorizations need not be unique. The catenary degree as defined in the paper determines the distance required to connect two irreducible factorizations of elements, and the tame degree is a version of the catenary degree.
Reviewer: Tero J. Harju (Turku)

Cited in 35 Documents

MSC:

20M14 Commutative semigroups
20M05 Free semigroups, generators and relations, word problems
11B75 Other combinatorial number theory

Keywords:

numerical monoids; irreducible factorizations; catenary degrees; tame degrees; finitely generated monoids; commutative cancellative monoids; minimal presentations; algorithms
PDF BibTeX XML Cite
\textit{S. T. Chapman} et al., Forum Math. 21, No. 1, 117--129 (2009; Zbl 1177.20070)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Apéry R., C. R. Acad. Sci. Paris 222 pp 1198– (1946)
[2] DOI: 10.1142/S0219498806001958 · Zbl 1115.20052
[3] Chapman S. T., Full Elasticity In Atomic Monoids And Integral Domains. Rocky Mountain J. Math. 36 pp 1437– (2006) · Zbl 1152.20048
[4] DOI: 10.1007/s00229-006-0008-8 · Zbl 1117.20045
[5] DOI: 10.1016/S0024-3795(01)00322-6 · Zbl 0995.20040
[6] Lambert J.-L., C. R. Acad. Sci. Paris Sér. I Math. 305 pp 2– (1987)
[7] DOI: 10.1007/BF03026549 · Zbl 0805.14015
[8] DOI: 10.2307/2032755 · Zbl 0071.03902
[9] DOI: 10.1142/S021819679600026X · Zbl 0863.20026
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.