4月8号下午5:30至6:30，我将在我校E17-129做个小讲座。特此感谢张栋童鞋(@菩提如是空 )和韦东奕童鞋的劳动。下面附上摘要、相关文献及讲义，希望内容比较不解自明。
Title: Polygon Problem
Abstract:
Given a simple polygon M with n+3 edges such that any three of its vertices are not collinear. Let M_d (resp. M_e) be the set of diagonals (resp. epigonals), i.e., chords which lie entirely in the interior (resp. exterior) of P. For 0 \le i \le n, let d_i (resp. e_i) be the number of i-subset of M_d (resp. M_e) whose elements are pairwise disjoint chords. We'll prove that if M is convex, then \sum (-1)^i d_i = (-1)^n; otherwise \sum (-1)^i d_i = \sum (-1)^i e_i =0.
References:
Lee, Carl W. "The associahedron and triangulations of the n-gon." European Journal of Combinatorics 10.6 (1989): 551-560.
Shephard, G. C. "A Polygon Problem." American Mathematical Monthly (1996): 505-507.
Devadoss, Satyan L., et al. "Visibility graphs and deformations of associahedra." arXiv preprint arXiv:0903.2848 (2009).
Barmak, Jonathan Ariel. "Star clusters in independence complexes of graphs."Advances in Mathematics 241 (2013): 33-57.
Notes:
MIT神
沧海老师
