“Parry–Sullivan invariant”的意思、由来-开放百科全书

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Parry–Sullivan invariant

释义

Definition
Properties
References

In mathematics, the Parry–Sullivan invariant (or Parry–Sullivan number) is a numerical quantity of interest in the study of incidence matrices in graph theory, and of certain one-dimensional dynamical systems. It provides a partial classification of non-trivial irreducible incidence matrices.

It is named after the English mathematician Bill Parry and the American mathematician Dennis Sullivan, who introduced the invariant in a joint paper published in the journal Topology in 1975.

Definition

Let A be an n × n incidence matrix. Then the Parry–Sullivan number of A is defined to be

where I denotes the n × n identity matrix.

Properties

It can be shown that, for nontrivial irreducible incidence matrices, flow equivalence is completely determined by the Parry–Sullivan number and the Bowen–Franks group.

References

{{cite journal | author=Parry, W., & Sullivan, D. | title=A topological invariant of flows on 1-dimensional spaces | journal=Topology | volume=14 | year=1975 | pages=297–299 | doi=10.1016/0040-9383(75)90012-9 | issue=4}}

4 : Dynamical systems|Matrices|Algebraic graph theory|Graph invariants

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