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        riddles >> putnam exam (pure math) >> (0,1) Matrices
        
(Message started by: THUDandBLUNDER on Jan 27^th, 2007, 7:37am)

Title: (0,1) Matrices
Post by THUDandBLUNDER on Jan 27^th, 2007, 7:37am

Define a (0,1) matrix A as a matrix whose entries are all either 0 or 1.

How many nxn (0,1) matrices are there such that A² is also a (0,1) matrix?

Title: Re: (0,1) Matrices
Post by Eigenray on Mar 9^th, 2007, 9:09am

I haven't done anything more than compute

2, 11, 172, 6327, [link=http://www.research.att.com/~njas/sequences/?q=2%2C11%2C172%2C6327&sort=0&fmt=0&language=english&go=Search]...[/link].

(Do you understand the meaning of [link=http://www.research.att.com/~njas/sequences/A122527]7 X n binary matrices[/link]?)

Title: Re: (0,1) Matrices
Post by THUDandBLUNDER on Mar 9^th, 2007, 9:39am

on 03/09/07 at 09:09:27, Eigenray wrote:

(Do you understand the meaning of [link=http://www.research.att.com/~njas/sequences/A122527]7 X n binary matrices[/link]?)

No, I don't have an answer for this one.

Title: Re: (0,1) Matrices
Post by Eigenray on Mar 9^th, 2007, 8:33pm

It's definitely [link=http://www.research.att.com/~njas/sequences/A121231]A121231[/link], which may or may not be the same as [link=http://www.research.att.com/~njas/sequences/A122527]A122527[/link], but I have no idea how the latter is the "number of 7 X n binary matrices," unless binary matrix means something else there. Presumably balakrishnan knows though.