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We consider a problem of maximizing the product of the sizes of two uniformcross-$t$-intersecting families of sets. We show that the value of this maximumis at most polynomially larger (in the size of a ground set) than a quantityconjectured by Hirschorn in 2008. At the same time, we observe that it can bestrictly bigger.

Uniform cross-$t$-intersecting families: proving Hirschorn's conjecture up to polynomial factor