Editing Binary relation (section)

=== Ferrers type ===
A [[strict order]] on a set is a homogeneous relation arising in [[order theory]].
In 1951 [[Jacques Riguet]] adopted the ordering of an [[integer partition]], called a [[Ferrers diagram]], to extend ordering to binary relations in general.<ref>J. Riguet (1951) "Les relations de Ferrers", [[Comptes Rendus]] 232: 1729,30</ref>

The corresponding logical matrix of a general binary relation has rows which finish with a sequence of ones. Thus the dots of a Ferrer's diagram are changed to ones and aligned on the right in the matrix.

An algebraic statement required for a Ferrers type relation R is
<math display="block">R \bar{R}^\textsf{T} R \subseteq R.</math>

If any one of the relations <math>R, \bar{R}, R^\textsf{T}</math> is of Ferrers type, then all of them are.
<ref name="Schmidt p.77">{{cite book|last1=Schmidt|first1=Gunther|last2=Ströhlein|first2=Thomas|title=Relations and Graphs: Discrete Mathematics for Computer Scientists|url={{google books |plainurl=y |id=ZgarCAAAQBAJ|paged=277}}|date=2012|publisher=Springer Science & Business Media|isbn=978-3-642-77968-8|authorlink1=Gunther Schmidt |page=77}}</ref>