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Square array of number of distinct m X n (0,1) matrices after iterated double sorting, read by antidiagonals.
0

%I #11 Dec 01 2023 03:25:52

%S 1,1,1,1,2,1,1,3,3,1,1,4,7,4,1,1,5,14,14,5,1,1,6,25,45,25,6,1,1,7,41,

%T 130,130,41,7,1,1,8,63,336,650,336,63,8,1,1,9,92,785,2942,2942,785,92,

%U 9,1,1,10,129,1682,11819,24520,11819,1682,129,10,1,1,11,175

%N Square array of number of distinct m X n (0,1) matrices after iterated double sorting, read by antidiagonals.

%C T(m,n) gives the number of distinct results obtained by repeatedly sorting the m X n (0,1) matrices by columns & then rows until reaching a fixed point. Its diagonal is A089006.

%e Array begins:

%e 1,1,1,1,1,...

%e 1,2,3,4,5,...

%e 1,3,7,14,25,...

%e 1,4,14,45,130,...

%e 1,5,25,130,650,...

%o (Haskell)

%o -- with the function "t" producing the array.

%o import List

%o prod = foldr (\x xs -> [y:ys | y <- x, ys <- xs]) [[]]

%o f xs = let ys = sort (transpose (sort (transpose xs))) in if xs == ys then xs else f ys

%o t m n = length $ nub $ map f $ prod (replicate m (prod (replicate n [0,1])))

%Y Cf. A089006.

%K nonn,tabl

%O 0,5

%A Randy Compton (RANDYRulerOfZexernet(AT)gmail.com), Dec 15 2009

%E Corrected & extended by Randy Compton (RANDYRulerOfZexernet(AT)gmail.com), Dec 18 2009