0,2

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.) - Ron Hardin (rhhardin(AT)att.net), May 08 2008

A result of Adolf Mader and Otto Mutzbauer shows that the two definitions are equivalent. - Victor 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.

Adolf Mader and Otto Mutzbauer, "Double Orderings of (0,1) Matrices", Ars Combinatorica v. 61 (2001) pp 81-95.

Ron Hardin, Binary arrays with both rows and cols sorted, symmetries

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}}.

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}]

Cf. A088672, A087981.

Sequence in context: A162049 A162050 A162051 this_sequence A019004 A027328 A111842

Adjacent sequences: A089003 A089004 A089005 this_sequence A089007 A089008 A089009

nonn

Wouter Meeussen (wouter.meeussen(AT)pandora.be), Nov 03 2003

a(6)-a(12) found by Ron Hardin (rhhardin(AT)att.net), 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 (njas(AT)research.att.com), Feb 05 2009 at the suggestion of Victor Miller