Abstract
A formal orthogonal pair is a pair (A, B) of symbolic rectangular matrices such that ABT = 0. 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.
| Original language | English |
|---|---|
| Article number | 68 |
| Number of pages | 12 |
| Journal | Seminaire Lotharingien de Combinatoire |
| Volume | 84B |
| Issue number | 84 |
| State | Published - 2020 |
| Event | The 32nd International Conference on Formal Power Series and Algebraic Combinatorics - Virtual Duration: 6 Jul 2020 → 24 Jul 2020 Conference number: 32 |
Keywords
- coherent configurations
- group cohomology
- Hadamard matrices
- representation theory
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
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