Báo cáo toán học: "Truncations of Random Unitary Matrices and Young Tableaux" docx

... regarding the moments and limiting distribution of the individual entries of a random unitary matrix. The matrix U k is called the kth truncation of U. Truncations of random unitary matri- ces have ... express the moments of Tr(U k ) in terms of the Weingarten function as follows: the electronic journal of combinatorics 14 (2007), #R21 6 Truncations of Random Unit...

Ngày tải lên: 07/08/2014, 15:22

... (x, y)ofelementsfromA n (respectively, S n ) such that the parts of Π are the orbits of the group x, y generated by x and y. Similarly let g A (Π) and g S (Π), respectively, be the number of pairs ... Odlyzko, Asymptotic enumeration methods, in “Handbook of Combinatorics (Vol.II)”(eds.:R.L.Graham,M.Gr¨otschel and L. Lov´asz), M.I.T. Press and North- Holland, 1995 (pp. 1063–1...

Ngày tải lên: 07/08/2014, 13:21

... Graphs” http://stat.berkeley.edu/users/aldous. [2] P.Diaconis and D.Freedman, Iterated Random Functions, SIAM Review 41 No. 1, p 45–76. [3] J.C.Hansen and J.Jaworski, Large Components of Random Mappings, Random Structures and Algorithms 17 ... such random maps. Lemma 4 Suppose h :[m] → [n] is selected uniformly at random from among the n m functions from [m] into [n] ,and l...

Ngày tải lên: 07/08/2014, 06:23

... is the analogue of the EKR theorem in the setting of the discrete cube endowed with the product measure. This useful theorem, and several generalizations thereof has been proven and reproven in ... journal of combinatorics 13 (2006), #N6 1 References [1] I. Dinur, S. Safra, On the importance of being biased (1.36 hardness of approximating Vertex-Cover). Annals of Mathematics,t...

Ngày tải lên: 07/08/2014, 13:21

... q-enumeration of ASM’s, which consists in counting ASM’s (or classes of symmetry of ASM’s) with respect to their number of −1 entries (to the number of orbits of −1 entries in the case of symmetric ... consequence of Equations (17) and (18) is that the total proportion of qQTASMs (of size 4N + 2) with two negative entries among the four central entries, is exactly the pro...

Ngày tải lên: 08/08/2014, 12:22

... interpretations of Z N , starting from (5) and using various properties of bijections of Foata and Zeilberger, Fran¸con and Viennot. Sections 4 and 5 respectively contain the t he two proofs of the exact ... the number of right-to-left maxima of σ and t(σ) is the number of r ig ht-to-left minima of σ, • asc(σ) is the number of ascents, i.e. integers i such that eit...

Ngày tải lên: 08/08/2014, 12:23

... Communi- cations of the Society of Mathematics, Kharkow (1892). [16] J. D. Mirzov, On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems ,Journalof Mathematical Analysis and Applications ... equations with retarded argument, Journal of Mathematical Analysis and Applications 41 (1973), no. 2, 293–299. [21] K. Taka ˆ si and M. Naito, On the number of zeros of...

Ngày tải lên: 22/06/2014, 21:20

... the logarithmic order of magnitude of the Ramsey-graph of Frankl and Wilson [5], continuing the sequence of results on new explicit Ramsey graph constructions of Alon [1] and Grolmusz [6]. Our ... integer between 0 and 5, and s ≤ c √ k. Since the (u, v) entry of ¯ A is the value (5), and (5) can be written as the sum of monomials in (7), matrix ¯ A can be written as th...

Ngày tải lên: 07/08/2014, 06:20

... Math. Soc., Providence, R.I., 1992, pp. 67–94. [Ke3] , The boundary of Young lattice and random Young tableaux,Formalpowerseries and algebraic combinatorics (New Brunswick, NJ, 1994), DIMACS Ser. ... integrand is symmetric in λ and µ. However, our assumptions on λ and µ are different: the depth of λ must be equal to d while µ is arbitrary. Actually, if the depth of µ is >...

Ngày tải lên: 07/08/2014, 06:20

... A representative of the left-hand side and the right-hand side of (1) for λ = 66532. Similarly, the right-hand side of (1) counts the number of pairs (c, G), where c ∈ C[λ] and G is a map from ... representative of the left-hand side and the right-hand side of (2) for λ = 87532. Similarly, the left-hand side of (2) counts the number of pairs (c, G ) , where c ∈ C ∗ [λ]...

Ngày tải lên: 08/08/2014, 14:23