Báo cáo toán học: "Asymptotics of generating the symmetric and alternating groups" docx

... Univ. Press, 1997). the electronic journal of combinatorics 12 (2005), #R56 5 Asymptotics of generating the symmetric and alternating groups John D. Dixon School of Mathematics and Statistics Carleton ... (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...

Ngày tải lên: 07/08/2014, 13:21

... n!  α  n α   σ∈S α Wg(d, n, σ) 4 Proof of the Main Theorem We are now in a position to prove Theorem 1. Proof. We work with the sum on the right hand side of Lemma 1. Plugging in the definition of the Weingarten function, ... ↑ S n S α is the induction of the trivial character of S α to S n . The final step in the proof relies on the characteristic map ch n : C...

Ngày tải lên: 07/08/2014, 15:22

... −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 increasing both in rows and in ... 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 P...

Ngày tải lên: 07/08/2014, 06:22

... 2007 Mathematics Subject Classification: 05A16 Abstract We generalize the classical work of de Bruijn, Knuth and Rice (giving the asymp- totics of the average height of Dyck paths of length n) to the ... representation of the zeta function ζ [7, section 1.12, (16)] in terms of Jacobi’s theta function θ. The appearance of ζ and θ in this context is not surprising f...

Ngày tải lên: 07/08/2014, 15:23

... desired. The proof of Theorem 3.10 is similar but uses Theorem 6.2 instead of Theorem 6.1. 4 Rewriting the expansion in terms of the original data To actually compute with the formulas in Theorems ... 0, then c is called nondegenerate. In the context of a single pair of appropriate c and α we will use the functions of Definition 3.1 without further introduction. Now f...

Ngày tải lên: 07/08/2014, 21:20

... in the study of the hook formula for various kinds of Young diagrams. The proof of 1.2 is based on the properties of shifted Schur functions[Ok.Ol ]which appeared in the asymptotic theory of the ... where s µ (x) is the ordinary Schur function. We remark that the paper[Ok.Ol ]was influenced by the work of Vershik and Kerov on the asymptotic theory of the r...

Ngày tải lên: 07/08/2014, 06:20

... dimension of the row-span of a matrix is equal to the dimension of its column-span, we can equally well study the dimension of the space spanned by the columns of the table. By the preceeding lemma, the N th entry ... that f λ (q) is the generating function for the entries of the column corresponding to the λ-cycles. The dimension of the column-span...

Ngày tải lên: 07/08/2014, 06:20

... (8.4) and (8.5). This completes the proof of the first part of Theorem 4. Equation (2.7) and the remark after the theorem follow from (8.1), provided we obtain formulas for C, λ and φ.(ThereisnoC ... implies the last claim in the theorem. 9 Proofs of Theorems 1 and 2 All mentions of Run(···) in Theorem 1 are divided by factorials and so can be thought of as func...

Ngày tải lên: 07/08/2014, 08:20

... a product of the r eciprocal of binomial coefficients, which satisfies the conditions of Theorems 1 and 2. A more general case of interest is when f(n, k) takes the fo rm of the product of functions ... true for D = C by the First Step. Split the sum in (1 ) into λn  k  (1 −λ)n and the rest, calling the first range of k the “center” and the rest the “ta...

Ngày tải lên: 08/08/2014, 11:20

Ngày tải lên: 05/08/2014, 15:21