Status of the Hadamard Circulant conjecture - MathOverflow

Status of the Hadamard Circulant conjecture

2011-02-15T15:45:17Z

The following feels like a community wiki question, so I do it here:

Recently we have heard of a new proof of the Circulant Hadamard conjecture of Ryser (a long standing difficult conjecture):

There is no Circulant Hadamard matrix with more than $4$ columns

see

http://blms.oxfordjournals.org/content/early/2011/01/24/blms.bdq112.abstract

More recently a gap was found in the proof:

see

http://people.math.sfu.ca/~jed/Papers/Craigen%20Jedwab.%20Circulant%20Hadamard.%20Preprint.pdf

Question: What is the real status of this Conjecture ?

Answer by Ken W. Smith for Status of the Hadamard Circulant conjecture

2011-05-11T02:43:50Z

The paper by Craigen and Jedwab points out a very definite flaw in the main theorem by Hurley, Hurley & Hurley, providing a counterexample to that theorem. So the conjecture is still open.

The paper by Leung and Schmidt (here) gives the latest information about possible counterexamples to the Circulant Hadamard conjecture.

A website of Bernhard Schmidt lists smallest open cases based (I believe) on the work of the paper cited above. The smallest open cases are, of course, quite large.

Answer by remote known for Status of the Hadamard Circulant conjecture

2011-09-29T23:16:06Z

On sep 4, 2011, authors Hurley, Hurley & Hurley of the paper on the Circulant Hadamard conjecture, has posted the same paper on the arxiv. Did they corrected the error reported by Craigen and Jedwab on feb 10, 2011?

Answer by Mark Yasuda for Status of the Hadamard Circulant conjecture

2011-12-05T00:16:43Z

Craigen and Jedwab have indicated that the September 2011 revision of Hurley, Hurley & Hurley also has a flaw:

http://people.math.sfu.ca/~jed/Papers/Craigen%20Jedwab.%20Circulant%20Hadamard%202.%20Preprint.pdf

Answer by Penguian for Status of the Hadamard Circulant conjecture

2011-12-11T23:23:41Z

About two weeks ago, at the International Workshop on Hadamard Matrices and Their Applications (RMIT), http://user.gs.rmit.edu.au/asha/iwhma/ Jennifer Seberry presented a proof, based on counting arguments http://user.gs.rmit.edu.au/asha/iwhma/html/Wednesday/JenniferSeberry.pdf, but that proof was quickly found to be incomplete. As far as I know, she is currently working on improving the proof. A special volume of the Australasian Journal of Combinatorics http://user.gs.rmit.edu.au/asha/iwhma/html/ajc.html is forthcoming, and with any luck, things will become much clearer at that point.

Answer by Luis H Gallardo for Status of the Hadamard Circulant conjecture

2011-12-16T22:54:01Z

check:

http://blms.oxfordjournals.org/content/early/2011/12/06/blms.bdq112