A140837 - OEIS

%I #4 Mar 30 2012 18:40:48

%S 1,1,2,6,23

%N Number of inequivalent indecomposable symmetric SQ matrices (strongly quadrangular) of order n.

%C Abstract: Strongly quadrangular matrices have been introduced in the study of the combinatorial properties of unitary matrices. It is known that if a (0, 1)-matrix supports a unitary then it is strongly quadrangular. However, the converse is not necessarily true. In this paper, we fully classify strongly quadrangular matrices up to degree 5. We prove that the smallest strongly quadrangular matrices which do not support unitaries have exactly degree 5. Further, we isolate two submatrices not allowing a (0, 1)-matrix to support unitaries.

%H Simone Severini and Ferenc Szollosi, <a href="http://arxiv.org/abs/0709.3651">A further look into combinatorial orthogonality</a>, arXiv:0709.3651

%K nonn

%O 1,3

%A _Jonathan Vos Post_, Jul 18 2008