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A089006
Number of distinct n X n (0,1) matrices after double sorting: by row, by column, by row .. until reaching a fixed point.
6
1, 2, 7, 45, 650, 24520, 2625117, 836488618, 818230288201, 2513135860300849, 24686082394548211147, 787959836124458000837941, 82905574521614049485027140026
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.
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}]
CROSSREFS
Column 0 of A374525.
Sequence in context: A162049 A162050 A162051 * A019004 A027328 A340450
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