Báo cáo toán học: "Threshold Functions for the Bipartite Tur´n Property a" potx

... =0|z=n 2 p)≤P(X=0|z≤n 2 p)≤3P(X=0)→0 by the theorem, where the last inequality above follows due to the observation that P(A|B) ≤ P(A)/P(B) and the fact that the central limit theorem [or the approxi- mate and ... = o(n 1/3 ); in the last two lines of the above calculation, the notation f  g means that f ≥ Kg for some positive constant K. This proves the theorem; as in...

Ngày tải lên: 07/08/2014, 06:20

... for the vertex set of G and |G| for |V (G)|; - E ( G ) for the edge set of G and e ( G) for |E (G)|; - d (u) for the degree of a vertex u; - δ (G) for the minimum degree of G; - k r (G) for the ... show that if G is a graph of order n, then the inequality e (G) > e (T r (n)) implies the inequality µ (G) > µ (T r (n)) . Therefore, Theorems 1-6 imply the corr...

Ngày tải lên: 07/08/2014, 21:21

... A 0 . Moreover, we note that at the start of the i’th step, |{j < i | p j < p i }| columns to the left of the column p i in the original A 0 have already been removed. Therefore, at the i’th step, when ... than the dimension of T . The second t r ansfer-matrix method shows that deg g d (z)  |Z| = 2 d−1 + 1 2  2d d  . (3) We have computed the generating functions...

Ngày tải lên: 08/08/2014, 01:20

... 2 to the terms of the sum, we conclude that each of them has the form (−1) m−k− 1 e k (u)p − m−k (u − k), and the Newton’s formula for elementary symmetric functions e m (u, τ) follows. The proof ... k, and the coefficients of these terms in the sum are exactly (−1) k−m (a 1 a 2 . . . a m ) −1 . Then from (6), the elementary symmetric functions are the sums of the prod...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 15:20

... between the path D and the main diagonal. For 0 ≤ i<n, define γ i (D) to be the number of cells between the path and the main diagonal in the i’th row of the picture, where we let the bottom ... path from the southwest corner to the northeast corner of the rectangle R a,b , we can keep track of both the area in R a,b below the path and the area in R a,b above...

Ngày tải lên: 07/08/2014, 08:22

... s µ (x  /y  ||a), implied by the combinatorial formula (2.14). Therefore, the required relation follows by comparing the two expansions. An explicit formula for the polynomials c ν λµ (a) is provided by the following ... symmetric functions of [21]; cf. formula (3.7) in that paper. Moreover, under the specialization a i = −i + 1 for all i ∈ Z the double Schur functio...

Ngày tải lên: 07/08/2014, 21:21

... q-analogues of Riemann’s ζ -functions, the Hurwitz ζ -functions and the Didichlet’s L -functions Now, by evaluating the kth derivative of both sides of Lemma 3.1 at t = 0, we obtain the following B k (q)=  d dt  k F q (t ... 10 of 16 Remark 3.2. The remarkable point is that the series on the right-hand side of Lemma 3.1 is uniformly convergent in the wider sense. From (2.1...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21