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

  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},
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
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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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  • 2013
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