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math.CO2025
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.CO2024
Cosystolic Expansion of Sheaves on Posets with Applications to Good 2-Query Locally Testable Codes and Lifted Codes
Uriya A. First, Tali Kaufman
We study sheaves on posets, showing that cosystolic expansion of such sheaves can be derived from local expansion conditions of the sheaf and the poset (typically a high dimensiona…
math.CO2024
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…