Can I read The System of Sets of Lengths and the Elasticity of Submonoids of a Finite-rank Free Commutative Monoid on EtoBox?

The System of Sets of Lengths and the Elasticity of Submonoids of a Finite-rank Free Commutative Monoid by Gotti, Felix is a Mathematics article available to read on EtoBox.

What is The System of Sets of Lengths and the Elasticity of Submonoids of a Finite-rank Free Commutative Monoid about?

Let [Formula: see text] be an atomic monoid. For [Formula: see text], let [Formula: see text] denote the set of all possible lengths of factorizations of [Formula: see text] into irreducibles. The system of sets of lengths of [Formula: see text] is the set [Formula: see text]. On the other hand, the elasticity of [Formula: see text], denoted by [Formula: see text], is the quotient [Formula: see text] and the elasticity of [Formula: see text] is the supremum of the set [Formula: see text]. The system of sets of lengths and the elasticity of [Formula: see text] both measure how far [Formula: see text] is from being half-factorial, i.e. [Formula: see text] for each [Formula: see text]. Let [Formula: see text] denote the collection comprising all submonoids of finite-rank free commutative monoids, and let [Formula: see text]. In this paper, we study the system of sets of lengths and the elasticity of monoids in [Formula: see text]. First, we construct for each [Formula: see text] a monoid in [Formula: see text] having extremal system of sets of lengths. It has been proved before that the system of sets of lengths does not characterize (up to isomorphism) monoids in [Formula: see text].

Who reads The System of Sets of Lengths and the Elasticity of Submonoids of a Finite-rank Free Commutative Monoid?

Author

Gotti, Felix

Publisher

World Scientific Publishing Company; World Scientific ; World Scientific Pub Co Pte Lt (ISSN 0219-4988)

Published

2019

Language

EN

Field

Mathematics (Physical Sciences)