Weisstein's Conjecture

On July 10, 2003, Eric Weisstein computed the numbers of n×n (0,1)-matrices all of whose eigenvalues are real and positive, obtaining counts for n=1, 2, ... of 1, 3, 25, 543, 29281, .... Based on agreement with OEIS A003024, Weisstein then conjectured that is equal to the number of labeled acyclic digraphs on n vertices.

This result was subsequently proved by McKay et al. (2003, 2004).

See also

(0,1)-Matrix, Acyclic Digraph, Positive Eigenvalued Matrix

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McKay, B. D.; Oggier, F. E.; Royle, G. F.; Sloane, N. J. A.; Wanless, I. M.; and Wilf, H. "Acyclic Digraphs and Eigenvalues of (0,1)-Matrices." 28 Oct 2003., B. D.; Royle, G. F.; Wanless, I. M.; Oggier, F. E.; Sloane, N. J. A.; and Wilf, H. "Acyclic Digraphs and Eigenvalues of (0,1)-Matrices." J. Integer Sequences 7, Article 04.3.3, 1-5, 2004., N. J. A. Sequence A003024/M3113 in "The On-Line Encyclopedia of Integer Sequences."

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Weisstein's Conjecture

Cite this as:

Weisstein, Eric W. "Weisstein's Conjecture." From MathWorld--A Wolfram Web Resource.

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