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Asymptotic Elasticity in Atomic Monoids

Authors:	Paul Baginski Scott T Chapman Matthew T Holden Terri A Moore

Institution:	(1) Department of Mathematics, University of California, Berkeley, 970 EvansHall #3840, Berkeley, CA 94720-3840, USA;(2) Trinity University, Department of Mathematics, One Trinity Place, San Antonio, Texas 78212-7200, USA;(3) Pomona College, Department of Mathematics, 610 N. College Way, Claremont, CA 91711, USA;(4) Present address: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637, USA;(5) University of Washington, Department of Mathematics, Seattle, WA 98195-4350, USA;(6) Present address: University of Nebraska, Department of Mathematics, 203 Avery Hall, P.O. Box 880130, Lincoln, NE 68588-0130, USA

Abstract:	Let M be a commutative atomic monoid (i.e. every nonzero nonunit of M can be factored as a product of irreducible elements). Let ρ(x) denote the elasticity of x ∈ M, R(M) = {ρ(x) \| x ∈ M} the set of elasticities of elements in M, and ρ(M) = sup R(M) the elasticity of M. Define \overline{ρ}(x) = lim_n→∞ ρ(xⁿ) to be the asymptotic elasticity of x. We determine some basic properties of the function \overline{ρ} and determine its image for certain block monoids.

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