Tag Archives: math

Coloring projective spaces and Ramsey theory

Posted on December 2, 2025 by 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 … Continue reading →

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory | Tagged , , , , , , , , , , , , | Leave a comment

Circular Sorting

Posted on November 4, 2025 by Anurag Bishnoi

How many swaps do you need to sort objects on a circle in clockwise order? This fairly simple and natural question quickly leads to some deep mathematics that I would like share. Let’s start with an example for : After … Continue reading →

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Constructing blocking sets using expander graphs and hypergraphs

Posted on November 19, 2024 by 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 … Continue reading →

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The Rank-Ramsey problem

Posted on November 18, 2024 by Anurag Bishnoi

The Ramsey number is the smallest such that every graph on vertices either contains a clique of size or an independent set of size . Ramsey’s theorem implies that these numbers always exist, and determining them (precisely or asymptotically) has … Continue reading →

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Ramsey numbers, polar spaces, and oddtowns

Posted on June 12, 2024 by Anurag Bishnoi

I have uploaded a preprint which concludes a joint work with John Bamberg and Ferdinand Ihringer that started last year during their visit to TU Delft. In this work, we have done one of my favorite things in mathematics research: … Continue reading →

Posted in Combinatorics, Extremal Combinatorics, Finite Geometry, Incidence Geometry, Ramsey Theory, Spectral Graph Theory | Tagged , , , , , , , , , , , , , , , , | 3 Comments