[seqfan] Unique Products Regarding Binary Matrices

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Thu Jun 10 13:24:54 CEST 2010

Say we have an n-by-n binary matrix (all elements either 0 or 1).

For a given row of the matrix, take the lengths of the runs of 0's and 1's and multiply these lengths. 
(By "run", it is meant a string of consecutive elements in the row (or column) all of the same value b, bounded by the value 1-b or by the edge of the row (or column).)

Do this for all rows and all columns to get 2n products.

Let a(n) = the number of such n-by-n binary matrices such that the 2n products are all unique.

I know that a(n) = 0 for n <= 8, since A034891(n) < 2n for n <= 8.

Is {a(n)} in the EIS already? It would seem a bad idea to compute this sequence via brute-force search of all the 2^(n^2) matrices for a given n, since the number of potential matrices grows so quickly as n grows.

Leroy Quet

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