2020/01/23 by Karni, Eyal, Kaufman, Tali
#05C65 #55U10 #Combinatorics (math.CO) #FOS: Mathematics #G.2.2
paper · doi:10.48550/arxiv.2001.08829
We wish to renew the discussion over recent combinatorial structures that are 3-uniform hypergraph expanders, viewing them in a more general perspective, shedding light on a previously unknown relation to the zig-zag product. We do so by introducing a new structure called triplet structure, that maintains the same local environment around each vertex. The structure is expected to yield, in some cases, a bounded family of hypergraph expanders whose 2-dimensional random walk converges. We have applied the results obtained here to several known constructions, obtaining a better expansion rate than previously known. Namely, we did so in the case of Conlon's construction and the S=[1,1,0] construction by Chapman, Linal and Peled.