These are a subset of "Circulant Matrices," the subject of a book of that title by Philip Davis, which may contain information you want. I don't know anything about their determinants. Steve Gray -----Original Message----- From: math-fun-bounces+stevebg=adelphia.net@mailman.xmission.com [mailto:math-fun-bounces+stevebg=adelphia.net@mailman.xmission.com] On Behalf Of Fred lunnon Sent: Monday, May 28, 2007 8:07 PM To: math-fun@mailman.xmission.com Subject: [math-fun] Cyclic 0-1 determinants A matrix A of order n is "cyclic" when A[i,j] is a function only of (i-j)(mod n), and "0-1" when A[i,j] € {0,1}. What is a criterion for such a matrix to be singular (over the integers)? What is the maximum absolute value of its determinant as a function of n? [Do I feel a OEIS-worthy sequence coming on?] Fred Lunnon