In mathematics, Ky Fan's lemma (KFL) is a combinatorial lemma about labellings of triangulations. It is a generalization of Tucker's lemma. It was proved by Ky Fan in 1952.[1]
In this example, where n = 2, there is no 2-dimensional alternating simplex (since the labels are only 1,2). Hence, there must exist a complementary edge (marked with red).
^"A Generalization of Tucker's Combinatorial Lemma with Topological Applications". The Annals of Mathematics. 56: 431. doi:10.2307/1969651.
variables over a fixed probability space. This topology is metrizable by the KyFan metric: d ( X , Y ) = inf { ε > 0 : P ( | X − Y | > ε ) ≤ ε } {\displaystyle...
reaction. KyFan norms: The sum of the k largest singular values of M is a matrix norm, the KyFan k-norm of M. The first of the KyFan norms, the KyFan 1-norm...
Pablo Parrilo, Motakuri Ramana, 2005) The Langlands–Shelstad fundamental lemma (Ngô Bảo Châu and Gérard Laumon, 2004) Milnor conjecture (Vladimir Voevodsky...
Escobar & Kaveh (2020). See, e.g., White (1923), page 520. Dines (1938). Fan, Ky (1959), Convex Sets and Their Applications. Summer Lectures 1959., Argon...
Math. 17 (1964), 101–134. Fan, Ky. A generalization of Tychonoff's fixed point theorem. Math. Ann. 142 (1960), 305–310. Fan, Ky. A minimax inequality and...
California Died: G. N. Watson, 79, English mathematician best known for Watson's lemma An 8.7 magnitude earthquake struck Alaska's Rat Islands at 7:01 p.m. local...
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