In mathematics, the ParryâSullivan invariant (or ParryâSullivan 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. [1] [2]
Let A be an n × n incidence matrix. Then the ParryâSullivan number of A is defined to be
where I denotes the n × n identity matrix.
It can be shown that, for nontrivial irreducible incidence matrices, flow equivalence is completely determined by the ParryâSullivan number and the BowenâFranks group.
In mathematics, the ParryâSullivan invariant (or ParryâSullivan 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. [1] [2]
Let A be an n × n incidence matrix. Then the ParryâSullivan number of A is defined to be
where I denotes the n × n identity matrix.
It can be shown that, for nontrivial irreducible incidence matrices, flow equivalence is completely determined by the ParryâSullivan number and the BowenâFranks group.