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
and also consider various stability conditions studied earlier for Krull monoids with finite divisor class group.
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
Advances in Applied Mathematics