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>limη(sn)nr(s)-1<∞ is constant on the Archimedean components of S. We apply the algorithm to show how to compute limη(sn)nr(s)-1 and also consider various stability conditions studied earlier for Krull monoids with finite divisor class group.
Document Object Identifier (DOI)
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, 438-453. doi: 10.1016/S0196-8858(02)00025-8
Advances in Applied Mathematics