Báo cáo toán học: " Robinson-Schensted correspondence for the signed Brauer algebras" pptx

... Robinson-Schensted correspondence for the signed Brauer algebra using bidomino tableau 4.1 The Knuth relations In this section, we derive the Knuth relations for the signed Brauer algebra by using the Robinson-Schensted ... give the method for translating the vacillating tableau to the bi-domino tableau. We also give the Knuth relations and the determin...

Ngày tải lên: 07/08/2014, 15:22

... 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 (2.13)and (2.14), we define the q-Bernoulli and ... formulas for the q-Bernoulli and q- Euler polynomials which will be used to prove the main results of this article. In Section 4, we construct the q-analogue of the Riemann’s ζ-...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 15:20

... =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

... several counting problems on the square lattice L n . There the authors gave the following bounds for the asymp- totics of f(n), the number of forests of L n ,andα(n), the number of acyclic orienta- tions ... proof gives the following Theorem 6.13. Let 2 ≤ k ≤ 8, then lim n→∞ (α(F k−1 n )) 1/n = ρ(D  k ). Finally, using Theorem 6.1 and Theorem 6.2 together with the last two...

Ngày tải lên: 07/08/2014, 07:21

... 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

... 10 has at least 3n−2 2 edges. The first one concerns the lower bound for the number of edges of MNH graphs. It is the combination of results proved in [2] and [7]. Theorem 1 (Bondy and Lin, Jiang, ... traceable for each e ∈ E( G). ∗ This material is based upon research for a thesis at the University of South Africa and is supported by the National Research Foundation under Gr...

Ngày tải lên: 07/08/2014, 13:21

... =  σ∈L x σ for each L ∈ L, the electronic journal of combinatorics 14 (2007), #R27 2 Lemma 4 a) If σ ∈ B ∗ 1 , then there exists L ∈ L ≥5 (see (4)) with σ ∈ L. b) If σ ∈ B ∗ 2 , then either there ... 4 resp. k = 5). In the case n = 7 the best previously known lower bound k 3 (7) ≥ 153 is due to Habsieger [5]. We show Theorem 1. k 3 (7) ≥ 156. For the case of 8 matches the best...

Ngày tải lên: 07/08/2014, 15:22

... holds for d − 1. We prove the claim for d. Let S = (G 1 , G 2 , . . . , G d ) be the sequence of the labels of the nodes u i , i ∈ [d], along the path P . Assume for the sake of contradiction ... {f }∪  i<d G i then by the observation made in the previous paragraph we are done, since this implies that S is a bad sequence. Therefore, we can assume for the rest of...

Ngày tải lên: 07/08/2014, 21:21

... 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 ... well as to an explicit formula for the c ν P, µ (a) in terms of the values of P ; see [19]. Therefore, the (dual) Littlewood–Richardson polynomials a...

Ngày tải lên: 07/08/2014, 21:21