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New Bounds for the Extreme Values of a Finite Sample of Real Numbers

โœ Scribed by Jean-Pierre Crouzeix; Alberto Seeger


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
189 KB
Volume
197
Category
Article
ISSN
0022-247X

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For a finite group G, let k G denote the number of conjugacy classes of G. We prove that a simple group of Lie type of untwisted rank l over the field of q ลฝ . l elements has at most 6 q conjugacy classes. Using this estimate we show that for ลฝ . ลฝ . 10 n completely reducible subgroups G of GL n, q

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## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph

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## Abstract The upper bound for the harmonious chromatic number of a graph given by Zhikang Lu and by C. McDiarmid and Luo Xinhua, independently (__Journal of Graph Theory__, 1991, pp. 345โ€“347 and 629โ€“636) and the lower bound given by D. G. Beane, N. L. Biggs, and B. J. Wilson (__Journal of Graph T