The Gwangju Combinatorics Seminar is a joint seminar series hosted by combinatorics groups in Chonnam National University and GIST, exploring recent research trends and mathematical ideas in various fields such as discrete mathematics, combinatorics, and graph theory.
This is the first talk of Gwangju Combinatorics Seminar. Bijective proof is an essential tool in discrete mathematics. In many instances, finding a suitable bijection is a key step of a proof.This talk introduces combinatorial bijections used to prove some properties of derangements, set partitions and pattern avoiding permutations.
We prove that for any circle graph H with at least one edge and for any positive integer k, there exists an integer t = t(k, H) such that every graph G either has a vertex-minor isomorphic to the disjoint union of k copies of H, or has a t-perturbation with no vertex-minor isomorphic to H.
Using the same techniques, we also prove that for any planar multigraph H, every binary matroid either has a minor isomorphic to the cycle matroid of kH, or is a low-rank perturbation of a binary matroid with no minor isomorphic to the cycle matroid of H.
This is joint work with Rutger Campbell, J. Pascal Gollin, Meike Hatzel, O-joung Kwon, Rose McCarty, and Sebastian Wiederrecht.
[GIST Math Colloquium]
Sep 26 (Fri) 13:00~14:00 Joonkyung Lee (Yonsei Univ)
Log-concavity in combinatorics
Log-concavity of discrete sequences often translates into intriguing negative correlations in random discrete structures. I will describe various examples that illustrate this phenomenon, ranging from classical to modern ones. If time permits, I will also discuss June E Huh's recent work on Lorentzian polynomials and how it applies to graph colouring problems, in connection with my own work with Jaeseong Oh and Jaehyeon Seo.
Nov 07 (Fri) 13:00~14:00 Jangsoo Kim (SKKU)
Combinatorics of orthogonal polynomials
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