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Over the past 50 years, cryptographers have constructed a number of surprising and important primitives like public-key encryption, which allows strangers to communicate privately even if eavesdroppers hear everything they say. However, there are...

The very first result ever proved about tournaments is due to Rédei, who nearly 100 years ago proved that every tournament contains a Hamiltonian directed path. Since then, questions and results about directed paths in tournaments have become a...

The regularity lemma says that every discrete object can be partitioned into a small number of random-like subobjects. But how small is small? And can we make small smaller if we assume that our given object is simple? And what does it mean for a...