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ramsey theory

Tight bounds on off-diagonal Ramsey numbers

Anurag Bishnoi

One of the oldest open problem in Ramsey theory has been solved. We now know the asymptotics of Ramsey numbers , for any fixed , up-to log factors. Last month, Domagoj Bradač showed that for any fixed and (where the term is hiding log factors), using a beautiful finite-geometric...

Coloring projective spaces and Ramsey theory

Anurag Bishnoi

What is the minimum number of colors needed to color the points of the Fano plane such that there is no monochromatic line? It is a nice exercise to prove that two colors do not suffice. This fact has been known at least since the 1956 paper of Richardson that introduced the notion of...

Constructing blocking sets using expander graphs and hypergraphs

Anurag Bishnoi

Blocking sets are one of the central topics in finite geometry, which was originally introduced in the context of game theory under the name of `blocking coalitions’: On Finite Projective Games. I first learned about them during my Ph.D. as a source of extremal problems that over the years as led...