Formal Orthogonal Pairs via Monomial Representations and Cohomology
Combinatorics
2020-06-03 v1
Abstract
A Formal Orthogonal Pair is a pair of symbolic rectangular matrices such that . It can be applied for the construction of Hadamard and Weighing matrices. In this paper we introduce a systematic way for constructing such pairs. Our method involves Representation Theory and Group Cohomology. The orthogonality property is a consequence of non-vanishing maps between certain cohomology groups. This construction has strong connections to the theory of Association Schemes and (weighted) Coherent Configurations. Our techniques are also capable for producing (anti-) amicable pairs. A handful of examples are given.
Keywords
Cite
@article{arxiv.2006.01197,
title = {Formal Orthogonal Pairs via Monomial Representations and Cohomology},
author = {Assaf Goldberger and Ilias Kotsireas},
journal= {arXiv preprint arXiv:2006.01197},
year = {2020}
}