학과 세미나 및 콜로퀴엄

대학원생 세미나

SAARC 세미나

편미분방정식 통합연구실 세미나

IBS-KAIST 세미나

학술회의 및 워크샵

학생 뉴스

북마크

Research Highlights

게시판

동문 뉴스

Problem of the week

Let \(P\) be a regular \(2n\)-gon. A perfect matching is a partition of vertex points into \(n\) unordered pairs; each pair represents a chord drawn inside \(P\). Two chords are said to "intersect" if they have a nonempty intersection.

Let \(X\) be the (random) number of intersection points (formed by intersecting chords) in a perfect matching chosen uniformly at random from the set of all possible matchings. Note that more than two chords can intersect at the same point, and in this case this intersection point is just counted once. Compute \(\lim_{n\rightarrow \infty} \frac{\mathbb E[X]}{n^2}\).

KAIST Compass
Biannual Research Webzine