기초과학연구원 이산수학그룹
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Suppose that $E$ is a subset of $\mathbb{F}_q^n$, so that each point is contained in $E$ with probability $\theta$, independently of all other points. Then, what is the probability that there is an $m$-dimensional affine subspace that contains at least $\ell$ points of $E$? What is the probability that $E$ intersects all $m$-dimensional affine subspaces? … |
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In 1975, Szemerédi proved that for every real number $\delta > 0 $ and every positive integer $k$, there exists a positive integer $N$ such that every subset $A$ of the set $\{1, 2, \cdots, N \}$ with $|A| \geq \delta N$ contains an arithmetic progression of length $k$. There has been a plethora of … |
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We introduce an odd coloring of a graph, which was introduced very recently, motivated by parity type colorings of graphs. A proper vertex coloring of graph $G$ is said to be odd if for each non-isolated vertex $x \in V (G)$ there exists a color $c$ such that $c$ is used an odd number of … |
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