Felix Gotti, Christopher O’Neill. Source: Journal of Commutative Algebra, Volume 12, Number 3, 319--331.Abstract:
Let [math] be an atomic monoid and let [math] be a non-unit element of [math] . The elasticity of [math] , denoted by [math] , is the ratio of its largest factorization length to its shortest factorization length, and it measures how far [math] is from having all its factorizations of the same length. The elasticity [math] of [math] is the supremum of the elasticities of all non-unit elements of [math] . In this paper, we study the elasticity of Puiseux monoids (i.e., additive submonoids of [math] ). We characterize, in terms of the atoms, which Puiseux monoids [math] have finite elasticity, giving a formula for [math] in this case. We also classify when [math] is achieved by an element of [math] . When [math] is a primary Puiseux monoid (that is, a Puiseux monoid whose atoms have prime denominator), we describe the topology of the set of elasticities of [math] , including a characterization of when [math] is a bounded factorization monoid. Lastly, we give an example of a Puiseux monoid that is bifurcus (that is, every nonzero element has a factorization of length at most [math] ).