A constructive proof of Ky Fan's generalization of Tucker's lemma
نویسندگان
چکیده
We present a constructive proof of Ky Fan’s combinatorial lemma concerning labellings of triangulated spheres. Our construction works for triangulations of Sn that contain a flag of hemispheres. As a consequence, we produce a constructive proof of Tucker’s lemma that holds for a larger class of triangulations than previous constructive proofs.
منابع مشابه
Some results on the block numerical range
The main results of this paper are generalizations of classical results from the numerical range to the block numerical range. A different and simpler proof for the Perron-Frobenius theory on the block numerical range of an irreducible nonnegative matrix is given. In addition, the Wielandt's lemma and the Ky Fan's theorem on the block numerical range are extended.
متن کاملFuzzy Linear Programming and its Application for a Constructive Proof of a Fuzzy Version of Farkas Lemma
The main aim of this paper is to deal with a fuzzy version of Farkas lemma involving trapezoidal fuzzy numbers. In turns to that the fuzzy linear programming and duality theory on these problems can be used to provide a constructive proof for Farkas lemma. Keywords Farkas Lemma, Fuzzy Linear Programming, Duality, Ranking Functions.
متن کاملOriented matroids and Ky Fan's theorem
L. Lovász has shown in [9] that Sperner’s combinatorial lemma admits a generalization involving a matroid defined on the set of vertices of the associated triangulation. We prove that Ky Fan’s theorem admits an oriented matroid generalization of similar nature (Theorem 3.1). Classical Ky Fan’s theorem is obtained as a corollary if the underlying oriented matroid is chosen to be the alternating ...
متن کاملC. 3i Working Paper Alfred P. Sloan School of Management a Unified Approach to Some Combinatorial Lemmas in Topology a Unified Approach to Some Combinatorial Lemmas in Topology
Part II of this study uses the path-following theory of labelled V-complexes developed in Part I to provide constructive algorithmic proofs of a variety of combinatorial lenmas in topology. \Je demonstrate two new dual lemmas on the n-dimensional cube, and use a Generc.lized S ^erner Lemma to prove a gener lization of the Knaster-Kuratowski-y.azurkiewicz Covering Lemma on the simplex. We also s...
متن کاملA Combinatorial Proof of Kneser's Conjecture
Kneser's conjecture, rst proved by Lovv asz in 1978, states that the graph with all k-element subsets of f1; 2; : : : ; ng as vertices and with edges connecting disjoint sets has chromatic number n ? 2k + 2. We derive this result from Tucker's combinatorial lemma on labeling the vertices of special triangulations of the octahedral ball. By specializing a proof of Tucker's lemma, we obtain self-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 111 شماره
صفحات -
تاریخ انتشار 2005