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Partitions, Diophantine equations, and control systems. (English) Zbl 1412.93022

Summary: Ordered partitions of elements of a reduced abelian monoid are defined and studied by means of the solutions of linear Diophantine equations. Links to feedback classification of linear dynamical systems over certain commutative rings are given in the same way as partitions of integers are related to feedback classification of linear dynamical systems over fields in the classical literature.

MSC:

93B25 Algebraic methods
05A17 Combinatorial aspects of partitions of integers
20M32 Algebraic monoids
93B10 Canonical structure

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References:

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