English

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

Commutative Algebra 2015-02-03 v1

Abstract

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 nn-dimensional state space and translate to the combinatorial problem of enumerating all the partitions of integer nn in some abelian semigroup. The problem of computing the number ν(n,k)\nu(n,k) of all the partitions of integer nn into kk different summands is pointed out.

Keywords

Cite

@article{arxiv.1502.00025,
  title  = {Partitions of elements in a monoid and its applications to systems theory},
  author = {Miguel V. Carriegos and Noemí DeCastro-García},
  journal= {arXiv preprint arXiv:1502.00025},
  year   = {2015}
}