primitive binary matrices?
Kennedy
kennedy at oldnews.org
Fri Aug 22 11:31:34 CEST 2003
I got:
1, 3, 139, 25575, 18077431
Kennedy
----- Original Message -----
From: "N. J. A. Sloane" <njas at research.att.com>
To: <seqfan at ext.jussieu.fr>
Cc: <njas at research.att.com>
Sent: Thursday, August 21, 2003 10:47 PM
Subject: primitive binary matrices?
>
> Would someone work out a few terms of the following
> sequence?
>
> It is probably not in the OEIS and it should be!
>
> a(n) = number of real n X n primitive (0,1)-matrices A.
>
> Primitive means that for some k, every element of A^k is
> strictly positive.
>
> It is known that you don't need to check values
> of k bigger than n^2 - 2n + 2
> (this is a theorem of Wielandt, that if A
> is primitive then k <= n^2 - 2n + 2)
>
> References - see A002522.
>
> The asymptotics are studied in the book
>
> Sachkov, V. N.; Tarakanov, V. E. Combinatorics of nonnegative matrices.
Translated from the 2000 Russian original by Valentin F. Kolchin.
Translations of Mathematical Monographs, 213. American Mathematical Society,
Providence, RI, 2002. x+269 pp. ISBN: 0-8218-2788-X (Reviewer: D. J.
Hartfiel) 15-02 (15A48)
>
> NJAS
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