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math.CO2022
A Counterexample to a Directed KKL Inequality
Quentin Dubroff, Shivam Nadimpalli, Bhargav Narayanan
We show that the natural directed analogues of the KKL theorem [KKL88] and the Eldan--Gross inequality [EG20] from the analysis of Boolean functions fail to hold. This is in contra…
math.CO2022
Reverse discrepancy and almost zero-sum stars
Quentin Dubroff
For chosen from the -valued functions on the edges of a hypergraph with , how large can one make $\min_{v \in V} |\sum_…
math.CO2022
Tower Gaps in Multicolour Ramsey Numbers
Quentin Dubroff, António Girão, Eoin Hurley +1
Resolving a problem of Conlon, Fox, and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their -colour and -colour Ramsey num…