Parry–Sullivan invariant

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. {{cite journal |first1=Bill |last1=Parry |author1-link=Bill Parry (mathematician) |first2=Dennis |last2=Sullivan |author2-link=Dennis Sullivan |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| doi-access= }}{{cite journal |title=An invariant of basic sets of Smale flows |first=Michael C. |last=Sullivan |journal=Ergodic Theory and Dynamical Systems |volume=17 |issue=6 |pages=1437–1448 |year=1997 |doi=10.1017/S0143385797097617|s2cid=96462227 |url=https://opensiuc.lib.siu.edu/cgi/viewcontent.cgi?article=1078&context=math_articles }}