Partitions of elements in a monoid and its applications to systems theory
| Autor: | Carriegos, Miguel V., DeCastro-García, Noemí |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $k$ different summands is pointed out. |
| Databáze: | arXiv |
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