# Partitions of elements in a monoid and its applications to systems theory

@article{Carriegos2015PartitionsOE,
title={Partitions of elements in a monoid and its applications to systems theory},
author={Miguel V. Carriegos and Noem'i DeCastro-Garc'ia},
journal={arXiv: Commutative Algebra},
year={2015}
}
• Published 30 January 2015
• Mathematics
• arXiv: Commutative Algebra
The feedback class of a locally Brunovsky linear system is fully determined by the decomposition of state space as direct sum of system invariants [4]. In this paper we attack the problem of enumerating all feedback classes of locally Brunovsky systems over a $n$-dimensional state space and translate to the combinatorial problem of enumerating all the partitions of integer $n$ in some abelian semigroup. The problem of computing the number $\nu(n,k)$ of all the partitions of integer $n$ into $k… Expand 4 Citations Partitions, diophantine equations, and control systems • Computer Science, Mathematics • Discret. Appl. Math. • 2019 Abstract Ordered partitions of elements of a reduced abelian monoid are defined and studied by means of the solutions of linear diophantine equations. Links to feedback classification of linearExpand A characterization of von Neumann rings in terms of linear systems • Mathematics • 2016 Abstract A new characterization of commutative von Neumann regular rings is given in terms of linear control systems having, locally, a Brunovsky Canonical Form. The problem of enumerating reachableExpand On partitions with$k$corners not containing the staircase with one more corner We give three proofs of the following result conjectured by Carriegos, De Castro-Garc\'ia and Munoz Castaneda in their work on enumeration of control systems: when$\binom{k+1}{2} \le n <Expand
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• Mathematics
• 2020
D. Napp was partially supported by the the Universitat d’Alacant (Grant No. VIGROB-287) and Generalitat Valenciana (Grant No. AICO/2017/128). V. Herranz and C. Perea were supported by the MinisterioExpand

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