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''László Pyber'' (born 8 May 1960 in Budapest) is a Hungarian mathematician. He works in combinatorics and group theory. He is a researcher at the Alfréd Rényi Institute of Mathematics, Budapest.He received the title the Doctor of Science from the Hungarian Academy of Sciences (1998). He won the Academics Prize (2007). == Main results== * He proved the conjecture of Paul Erdős and Tibor Gallai, that the edges of any simple graph with ''n'' vertices can be covered with at most ''n''-1 circuits and edges. * He proved the following conjecture Paul Erdős. Any graph with ''n'' vertices and its complement can be covered with ''n''2/4+2 cliques. * He proved a ''c''log2''n'' bound to the size of a minimal base of a primitive permutation group of degree ''n'' not containing ''A''''n''. * He gave the following estimate of the number of groups of order ''n''. If the prime power decomposition of ''n'' is ''n''=''p''1''g''1 ⋯ ''p''''k''''g''''k'' and μ=max(''g''1,...,''g''k), then the number of nonisomporphic ''n''-element groups is at most * Łuczak and Pyber proved the following conjecture of McKay. For every, ε>0 there is a number ''c'' such that for all sufficiently large ''n'', ''c'' randomly chosen elements generate the symmetric group ''S''''n'' with probability greater than 1-ε. * A result also proved by Łuczak and Pyber states that almost every element of ''S''''n'' does not belong to a transitive subgroup different from ''S''''n'' and ''A''''n'' (conjectured by Cameron). * Solving a problem of subgroup growth he proved that for every nondecreasing function ''g''(''n'')≤log(''n'') there is a residually finite group generated by 4 element, whose growth type is . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「László Pyber」の詳細全文を読む スポンサード リンク
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