A further look into combinatorial orthogonality

2007/09/23 by Simone Severini, Severini, Simone, Ferenc Szöllősi +1
Mathematics · Physics and Astronomy · #05B20 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph) #math.CO #msc:05B20 #quant-ph

paper · pdf · doi:10.48550/arxiv.0709.3651

11 pages, some typos are corrected. To appear in The Electronic journal of Linear Algebra

arxiv created 2008/07/16 · arxiv updated 2009/12/01

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.

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