ELA, Volume 12, pp. 6-16, December 2004, abstract.
A Bruhat Order for the Class of (0,1)-Matrices with
Row Sum Vector R and Column Sum Vector S
Richard A. Brualdi and Suk-Geun Hwang
Generalizing the Bruhat order for permutations
(so for permutation matrices), a Bruhat order is
defined for the class of m by n (0,1)-matrices
with a given row and column sum vector. An algorithm
is given for constructing a minimal matrix (with
respect to the Bruhat order) in such a class. This
algorithm simplifies in the case that the row and
column sums are all equal to a constant k. When k=2
or k=3, all minimal matrices are determined. Examples
are presented that suggest such a determination might
be very difficult for k >= 4.