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The eigenvalues of random symmetric matrices
It is shown that with probability 1-o(1)all eigenvalues belong to the above intervalI if μ=0, while in case μ>0 only the largest eigenvalueλ1 is outsideI, and λ1 asymptotically has a normal distribution with expectation (n−1)μ+v+(σ2/μ) and variance 2σ2 (bounded variance!). Expand
Davenport-Schinzel theory of matrices
Among other results it is proved that f ( n ; 1 1 11 1 ) = Θ ( α ( n ) n ), where α( n ) is the inverse of the Ackermann function. Expand
Extremal problems whose solutions are the blowups of the small witt-designs
It is shown that the only optimal families, i.e., ∥F∥ = f(k, n, Σ) arise from the unique (11, 5, 4) or (12, 6, 5) Steiner-systems by a simple operation, called blowup. Expand
New Asymptotics for Bipartite Turán Numbers
  • Z. Füredi
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 July 1996
An exact result for 3-graphs
This paper proves Theorem 1 which gives a full description of families of 3-subsets in which any 4 points contain 0 or 2 members of the family. Expand
Exact solution of some Turán-type problems
The validity of this conjecture is established for n ⩾ n 0 ( k), in a more general framework, when the excluded configuration is a fixed sunflower. Expand
A new generalization of the Erdős-Ko-Rado theorem
This paper shows that the Erdős-Ko-Rado theorem holds forn>n0(k) if and only ifs≧2k, and sharpens a theorem of Bollobás. Expand
The Greatest Angle Among n Points in the d- Dimensional Euclidean Space
There exists a pointset of cardinality at least 1.15 4 in E d such that all angles determined by the triples of are less than π/2. This disproves the old conjecture that | ≤ 2 d - 1.
Forbidding Just One Intersection
It is shown that if F is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ⩾ 2l + 2 and n sufficiently large F with equality holding if and only if F consists of all the k-sets containing a fixed (l + 1)-set. Expand
Families of finite sets in which no set is covered by the union ofr others
AbstractLetfr(n, k) denote the maximum number ofk-subsets of ann-set satisfying the condition in the title. It is proved that $$f_1 (n,r(t - 1) + 1 +Expand