Document Type
Article
Publication Date
10-2002
Abstract
Let S be a reduced commutative cancellative atomic monoid. If s is a nonzero element of S, then we explore problems related to the computation of η(s), which represents the number of distinct irreducible factorizations of s∈S. In particular, if S is a saturated submonoid of Nd, then we provide an algorithm for computing the positive integer r(s) for which
0 < limn→∞η(sn)nr(s)-1∞.
We further show that r(s) is constant on the Archimedean components of S. We apply the algorithm to show how to compute
limn→∞η(sn)nr(s)-1
and also consider various stability conditions studied earlier for Krull monoids with finite divisor class group.
Identifier
10.1016/S0196-8858(02)00025-8
Publisher
Elsevier Science
Repository Citation
Chapman, S.T., García-García, J.I., García-Sánchez, P.A., & Rosales, J.C. (2002). On the number of factorizations of an element in an atomic monoid. Advances in Applied Mathematics, 29(3), 438-453. doi:10.1016/S0196-8858(02)00025-8
Publication Information
Advances in Applied Mathematics