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In this note, we give a self-contained and elementary proof of the elementaryconstruction of spectral high-dimensional expanders using elementary matricesdue to Kaufman and Oppenheim [Proc. 50th ACM Symp. on Theory of Computing(STOC), 2018]. As a bonus, this also yields a simple construction and analysisof standard expanders.

A note on the elementary construction of High-Dimensional Expanders of Kaufman and Oppenheim