기초과학연구원 이산수학그룹
On October 29, 2024, Felix Christian Clemen from the IBS Extremal Combinatorics and Probability Group gave a talk on an upper bound for the number of triangles almost congruent to a fixed triangle among n points at the Discrete Math Seminar. The title of his talk was “Triangles in the Plane.”
A classical problem in combinatorial geometry, posed by Erdős in 1946, asks to determine the maximum number of unit segments in a set of $n$ points in the plane. Since then a great variety of extremal problems in finite planar point sets have been studied. Here, we look at such questions concerning triangles. Among others we answer the following question asked by Erdős and Purdy almost 50 years ago: Given $n$ points in the plane, how many triangles can be approximate congruent to equilateral triangles?
For our proofs we use hypergraph Turán theory. This is joint work with Balogh and Dumitrescu.
The IBS Discrete Mathematics Group welcomes Dr. Felix Christian Clemen, a new research fellow at the IBS Extremal Combinatorics and Probability Group, from August 16, 2024. He received his Ph.D. from the University of Illinois at Urbana-Champaign under the supervision of Prof. József Balogh. He is interested in extremal combinatorics, combinatorial geometry, and probabilistic combinatorics.