Báo cáo toán học: " ASYMPTOTICS OF THE NUMBER OF k-WORDS WITH AN -DESCENT" pot

... holds and so, case LC implies (c). 5.ProofofTheorem3 Proof (of (a)): If R = 0, there is nothing to prove. Otherwise, the hypothesis asserts that [x n ] C(x) 2 ≤ [x n ] MC(x)forsomeM<∞ and n ... of the surface, B depends on the type of map, and A depends on both the type of map and the surface. See [22] for a proof of (7) for the unrooted case and for further references...

Ngày tải lên: 07/08/2014, 06:20

... class="bi x0 y0 w1 h 1" alt =""

Ngày tải lên: 05/08/2014, 15:20

... tableaux of shape µ of size k is the multiplicity of the representation with highest weight µ in the kth tensor power of the defining representation of GL n , the number of up-down tableaux of shape ... because the allowed tableaux are different for each n. The problem with an unlimited number of rows is not meaningful, as the last row can never be used...

Ngày tải lên: 07/08/2014, 08:22

... behavior of the given sum, for fixed s and n →∞, with the asymptotic behavior of a hypothetical closed form, and to show that the two could never be the same. In Cusick [Cus] there is a method that can, ... 2r)  p r  . But then one can verify that the coefficient of the first power of k in the polynomial on the left of (3) is (−1) p−1 (p − r)/(p − 2r), while the co...

Ngày tải lên: 07/08/2014, 06:22

... provide the exact value of the Ramsey numbers R(P n 1 , P n 2 , . . . , P n t , C k ) for certain values of n i and k and then we determine the exact values of some three-color Ramsey numbers ... 3. Proof. Consider the graph K m−1 ∪ K 3 and color the complete graphs K m−1 and K 3 by color red. Consider two vertices of K 3 , say u, v, and color the edges which are incident...

Ngày tải lên: 08/08/2014, 12:23

... of k (the positions of the last q − 1 copies of k do not affect the number of occurrences of the pattern), a nd we let A = a b−(q− 1) . The number of occurrences of 1 ′ 2 p,q that the k’s of σ ... one of the first p letters is k. By the principle of inclusion-exclusion, the number of such σ is p  m=1 N m (−1) m+1 , where N m is the sum, over all m...

Ngày tải lên: 08/08/2014, 14:23

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Ngày tải lên: 05/08/2014, 09:46

... associated with strips of Young diagrams, Adv. in Math. 41 (1981), 115–136. ASYMPTOTICS OF THE NUMBER OF k-WORDS WITH AN -DESCENT Amitai Regev ∗ Department of Mathematics The Pennsylvania State ... −1)! Standard and Semistandard Tableaux. Let λ  n (i.e. λ is a partition of n). A tableau of shape λ, filled with 1, ···,n, is standard if the numbers in it are inc...

Ngày tải lên: 07/08/2014, 06:22

... (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 ... than two generators In view of the theorem of M. Hall mentioned in Remark 3 there is some interest in extending the analysis for t n to the case of r generators whe...

Ngày tải lên: 07/08/2014, 13:21

... related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bulletin of the American Math. Soc., 38:435–465, 2001. [3] N. Bonichon and M. Mosbah. Watermelon uniform random generation ... discussions, and to the anonymous referee for helpful suggestions and corrections and for drawing my attention to the paper of Biane, Pitman and Yor [2]. 2 Exact enumeration F...

Ngày tải lên: 07/08/2014, 15:23