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math.CO2022★ 1 cited
On Good -Query Locally Testable Codes from Sheaves on High Dimensional Expanders
Uriya A. First, Tali Kaufman
We expose a strong connection between good -query locally testable codes (LTCs) and high dimensional expanders. Here, an LTC is called good if it has constant rate and linear di…
math.CO2022
The Cheeger Inequality and Coboundary Expansion: Beyond Constant Coefficients
Uriya A. First, Tali Kaufman
The Cheeger constant of a graph, or equivalently its coboundary expansion, quantifies the expansion of the graph. This notion assumes an implicit choice of a coefficient group, nam…
math.RA2022
Azumaya Algebras With Orthogonal Involution Admitting an Improper Isometry
Uriya A. First
Let be an Azumaya algebra with orthogonal involution over a ring with . We show that if admits an improper isometry, i.e., an element wi…