A further look into combinatorial orthogonality

Details A further look into combinatorial orthogonality A further look into combinatorial orthogonality

2007-09-23

arxiv.org/abs/0709.3651v2

Mathematics

Combinatorics

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

Scientific paper

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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