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I am looking for a hypergraphs product of hypergraph H1,H2 that preserves some expansion properties of H1,H2. The expansion property I am looking at is HD-random walk. The product I am looking for is similar to normal hypergraph product, that is similar to a cartesian product, but not very much.

I work in the specific case where H2 is 4-complete hypergraph and H1 is a 3-uniform hypergraph that expands.

I am working on proving that the normal product is OK, but I don't want to reinvent the wheel.

Thanks.

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  • $\begingroup$ What is "HD-random walk"? I can't find this anywhere. $\endgroup$
    – YCor
    Commented Feb 10, 2020 at 17:23
  • $\begingroup$ High dimensional random walk. For example, see here: arxiv.org/abs/1604.02947. Basically, in the limited case of 3-uniform, it is a random walk on the graph of 2-edges where $e' \sim e$ if $e' \cup e \in T(H)$. $T(H)$ are the triplets/ 3-edges. $\endgroup$
    – user2679290
    Commented Feb 10, 2020 at 17:32
  • $\begingroup$ I just say that I found such a candidate construction and proved its expansion properties in the simplest case. To be declared in a future paper. $\endgroup$
    – user2679290
    Commented Mar 10, 2020 at 21:22

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