|
|
| Line 1: |
Line 1: |
| In [[mathematics]], the '''Parry–Sullivan invariant''' (or '''Parry–Sullivan number''') is a numerical quantity of interest in the study of [[incidence matrix|incidence matrices]] in [[graph theory]], and of certain one-dimensional [[dynamical systems]]. It provides a partial classification of non-trivial irreducible incidence matrices.
| | Oscar is how he's known as and he totally enjoys this title. South Dakota is exactly where me and my spouse live. Managing individuals is his occupation. To collect cash is 1 of the issues I adore most.<br><br>My web site :: [http://www.alhuloul.com/?p=235037 alhuloul.com] |
| | |
| It is named after the English mathematician [[Bill Parry (mathematician)|Bill Parry]] and the American mathematician [[Dennis Sullivan]], who introduced the invariant in a joint paper published in the journal [[Topology (journal)|''Topology'']] in 1975.
| |
| | |
| ==Definition==
| |
| | |
| Let ''A'' be an ''n'' × ''n'' incidence matrix. Then the '''Parry–Sullivan number''' of ''A'' is defined to be
| |
| | |
| :<math>\mathrm{PS} (A) = \det (I - A), \, </math>
| |
| | |
| 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}}
| |
| | |
| {{DEFAULTSORT:Parry-Sullivan invariant}}
| |
| [[Category:Dynamical systems]]
| |
| [[Category:Matrices]]
| |
| [[Category:Algebraic graph theory]]
| |
| [[Category:Graph invariants]]
| |
Latest revision as of 05:36, 13 October 2014
Oscar is how he's known as and he totally enjoys this title. South Dakota is exactly where me and my spouse live. Managing individuals is his occupation. To collect cash is 1 of the issues I adore most.
My web site :: alhuloul.com