English

A further look into combinatorial orthogonality

Combinatorics 2008-07-17 v2 Quantum Physics

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.

Keywords

Cite

@article{arxiv.0709.3651,
  title  = {A further look into combinatorial orthogonality},
  author = {Simone Severini and Ferenc Szöllősi},
  journal= {arXiv preprint arXiv:0709.3651},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T09:20:45.175Z