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arXiv · 2509.14463

Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture

Kean Fallon
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Abstract

We introduce the notion of equiangular tight frames in real symplectic spaces and formulate a conjecture on their existence in terms of the dimension and number of vectors. Our main results shows the "symplectic Zauner's conjecture" is equivalent to the skew Hadamard conjecture. The proof involves counting subgraphs called "diamonds" in tournaments.

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Kean Fallon. 2025-09-17. Equiangular tight frames in real symplectic space: Zauner's conjecture and the skew Hadamard conjecture. https://arxiv.org/abs/2509.14463

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