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A theorem on permutation graphs with applications

โœ Scribed by Yu Chang-Wu; Chen Gen-Huey


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
906 KB
Volume
77
Category
Article
ISSN
0020-0255

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## Abstract A semicycle is said to turn at a point __a__ if the arcs incident to __a__ are both to it or both from it. We prove that if a nonempty set of points of a finite directed graph contains a turning point of each semicycle, then one of its members is a turning point of every semicycle to wh

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A unified martingale approach is presented for establishing the asymptotic normality of some sequences of random variables. It is applied to the numbers of inversions, rises, and peaks, respectively, as well as the oscillation and the sum of consecutive pair products of a random permutation.