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An approximation of partial sums of independent RV'-s, and the sample DF. I
SummaryLet Sn=X1+X2+⋯+Xnbe the sum of i.i.d.r.v.-s, EX1=0, EX12=1, and let Tn= Y1+Y2+⋯+Ynbe the sum of independent standard normal variables. Strassen proved in [14] that if X1 has a finite fourthExpand
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Blow-up Lemma
Regular pairs behave like complete bipartite graphs from the point of view of bounded degree subgraphs. Expand
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The eigenvalues of random symmetric matrices
We show that with probability 1-o(1)all eigenvalues belong to the above intervalI if μ=0, while in case μ>0 only the largest eigenvalue λ1 is outsideI. Expand
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Szemeredi''s Regularity Lemma and its applications in graph theory
Szemer\''edi''s Regularity Lemma is an important tool in discrete mathematics. It says that, in some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps inExpand
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A Note on Ramsey Numbers
We prove R(3, x) cx 2 ln x and, for each k ⩾ 3, R(k,x) c k x k − 2 asymptotically in x . Expand
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Storing a sparse table with O(1) worst case access time
We describe a data structure for representing a set of n items from a universe of m items, which uses space n+o(n) and accommodates membership queries in constant time. Expand
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A generalization of a problem of Steinhaus
This is the fixed version of an article made available by an organization that acts as a publisher by formally and exclusively declaring the article "published". If it is an "early release" articleExpand
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On the probability that a random ±1-matrix is singular
We report some progress on the old problem of estimating the probability, Pn, that a random n× n ± 1 matrix is singular: Theorem. There is a positive constant ε for which Pn < (1− ε)n. This is aExpand
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Proof of the Seymour conjecture for large graphs
Paul Seymour conjectured that any graphG of ordern and minimum degree of at leastk/k+1n contains thekth power of a Hamiltonian cycle. Here, we prove this conjecture for sufficiently largen.
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