기초과학연구원 이산수학그룹
For the past few years, I've been working on formalizing proofs in matroid theory using the Lean proof assistant. This has led me to many interesting and unexpected places. I'll talk about what formalization looks like in practice from the perspective of a combinatorialist.
The 2024 Workshop on (Mostly) Matroids will be held in-person at the Institute for Basic Science (IBS), Daejeon, South Korea, from August 19, 2024 to August 23, 2024. We expect that most people would arrive on Sunday, August 18 and leave on Saturday, August 24. Our hope is that this workshop will continue the tradition …
Every (finite) matroid consists of a (finite) set called the ground set, and a collection of distinguished subsets called the independent sets. A classic example arises when the ground set is a finite set of vectors from a vector space, and the independent subsets are exactly the subsets that are linearly independent. Any such matroid …
Website: https://cw2024.combinatorics.kr/ Location Chungbuk National University, Cheongju, Korea. Advisory Committee Committee of Discrete Mathematics, The Korean Mathematical Society (Chair: Sang-il Oum, IBS Discrete Mathematics Group / KAIST) Sponsors IBS Discrete Mathematics Group. Korean Mathematical Society
In 1980, Burr conjectured that every directed graph with chromatic number $2k-2$ contains any oriented tree of order $k$ as a subdigraph. Burr showed that chromatic number $(k-1)^2$ suffices, which was improved in 2013 to $\frac{k^2}{2} - \frac{k}{2} + 1$ by Addario-Berry et al. In this talk, we give the first subquadratic bound for Burr's …
An edge-colored graph $H$ is called rainbow if all of its edges are given distinct colors. An edge-colored graph $G$ is then called rainbow $H$-free when no copy of $H$ in $G$ is rainbow. With this, we define a graph $G$ to be rainbow $H$-saturated when there is some proper edge-coloring of $G$ which is rainbow $H$-free, …
We prove the following variant of Helly’s classical theorem for Hamming balls with a bounded radius. For $n > t$ and any (finite or infinite) set $X$, if in a family of Hamming balls of radius $t$ in $X$, every subfamily of at most $2^{t+1}$ balls have a common point, so do all members of …
We say that a 0-1 matrix A contains another such matrix (pattern) P if P can be obtained from a submatrix of A by possibly changing a few 1 entries to 0. The main question of this theory is to estimate the maximal number of 1 entries in an n by n 0-1 matrix NOT …
Rödl and Ruciński established Ramsey's theorem for random graphs. In particular, for fixed integers $r$, $\ell\geq 2$ they showed that $n^{-\frac{2}{\ell+1}}$ is a threshold for the Ramsey property that every $r$-colouring of the edges of the binomial random graph $G(n,p)$ yields a monochromatic copy of $K_\ell$. We investigate how this result extends to arbitrary colourings …
In general, random walks on fractal graphs are expected to exhibit anomalous behaviors, for example heat kernel is significantly different from that in the case of lattices. Alexander and Orbach in 1982 conjectured that random walks on critical percolation, a prominent example of fractal graphs, exhibit mean field behavior; for instance, its spectral dimension is …