기초과학연구원 이산수학그룹
Let $Q_n$ be the $n$-dimensional Hamming cube (hypercube) and $N=2^n$. We prove that the number of maximal independent sets in $Q_n$ is asymptotically $2n2^{N/4}$, as was conjectured by Ilinca and Kahn in connection with a question of Duffus, Frankl and Rödl. The value is a natural lower bound derived from a connection between maximal independent …
Combinatorics Workshop (조합론 학술대회) is the biggest annual conference in combinatorics in Korea. It was firstly held in 2004 by the Yonsei University BK21 Research Group. It has been advised by the committee of discrete mathematics of the Korean Mathematical Society since 2013. The aim of this workshop is to bring active researchers with different …
A special session "Extremal and Probabilistic Combinatorics" at the 2021 KMS Spring Meeting is organized by Tuan Tran. URL: https://www.kms.or.kr/meetings/spring2021/ Speakers and Schedule All talks are on April 30. Joonkyung Lee (이준경), University College London Majority dynamics on sparse random graphs Dong Yeap Kang (강동엽), Unversity of Birmingham The Erdős-Faber-Lovász conjecture and related results Jinyoung …
Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its "expectation-threshold," which is a natural (and often easy to calculate) lower bound on the threshold. …
Thresholds for increasing properties of random structures are a central concern in probabilistic combinatorics and related areas. In 2006, Kahn and Kalai conjectured that for any nontrivial increasing property on a finite set, its threshold is never far from its "expectation-threshold," which is a natural (and often easy to calculate) lower bound on the threshold. …
The Dedekind's Problem asks the number of monotone Boolean functions, a(n), on n variables. Equivalently, a(n) is the number of antichains in the n-dimensional Boolean lattice $^n$. While the exact formula for the Dedekind number a(n) is still unknown, its asymptotic formula has been well-studied. Since any subsets of a middle layer of the Boolean …