extremal combinatorics

Mar 10

Small complete cap sets

Anurag Bishnoi

The following post is (partly) based on discussions with Dion Gijswijt and Ananth Ravi from September 2025. The famous cap set problem has attracted the attention of various mathematicians from different areas over the last few decades. It asks for the largest possible size, , of a 3-term...

mathematics combinatorics complete caps extremal combinatorics projective caps dion gijswijt extremal problems affine caps cap set finite geometry finite fields

Dec 02 2025

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...

mathematics math combinatorics extremal combinatorics caps ramsey theory incidence geometry extremal problems chromatic number vector spaces sum-free sets ramsey blocking set finite geometry finite fields ramsey numbers