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

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.


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