OFFSET
0,2
COMMENTS
Also, number of n X n binary matrices with both rows and columns, considered as binary numbers, in nondecreasing order. (Ordering only rows gives A060690.) - R. H. Hardin, May 08 2008
A result of Adolf Mader and Otto Mutzbauer shows that the two definitions are equivalent. - Victor S. Miller, Feb 03 2009
For n=5, only 0.07% remain distinct. Sorting columns and\or rows does not change the permanent of the matrix and leaves the absolute value of the determinant unchanged.
Diagonal of A180985.
REFERENCES
Adolf Mader and Otto Mutzbauer, "Double Orderings of (0,1) Matrices", Ars Combinatoria v. 61 (2001) pp 81-95.
LINKS
R. H. Hardin, Binary arrays with both rows and cols sorted, symmetries
M. Werner, An Algorithmic Approach for the Zarankiewicz Problem, Slides, 2012. - From N. J. A. Sloane, Jan 01 2013
EXAMPLE
The 7 (2 X 2)-matrices are {{0,0},{0,0}}, {{0,0},{0,1}}, {{0,0},{1,1}}, {{0,1},{0,1}}, {{0,1},{1,0}}, {{0,1},{1,1}} and {{1,1},{1,1}}.
MATHEMATICA
baseform[li_List] := FixedPoint[Sort[Transpose[Sort[Transpose[Sort[ #1]]]]]&, li]; Table[Length@Split[Sort[baseform/@(Partition[ #, n]&/@(IntegerDigits[Range[0, -1+2^n^2], 2, n^2]))]], {n, 4}]
KEYWORD
nonn,hard,more
AUTHOR
Wouter Meeussen, Nov 03 2003
EXTENSIONS
a(6)-a(12) found by R. H. Hardin, May 08 2008. These terms were found using bdd's (binary decision diagrams), just setting up the logical relations between bits in a gigantic bdd expression and using that to count the satisfying states.
Edited by N. J. A. Sloane, Feb 05 2009 at the suggestion of Victor S. Miller
STATUS
approved