Báo cáo toán học: " Character Polynomials, their q-analogs and the Kronecker product" potx

... and (n − |ν|, ν) are partitions for all n ≥ 2k since the hypotheses |µ|, |ν| ≤ k the electronic journal of combinatorics 16(2) (2009), #R19 20 Character Polynomials, their q-analogs and the Kronecker ... #R19 1 The c λ,µ,ν go by the name of Kronecker coeffici ents” and they may be interpreted as the multiplicity of the irreducible representation of S n indexed by...

Ngày tải lên: 08/08/2014, 01:20

... of the Aztec diamond graph A, define the weight of the matching (m) to be the product of the weights of all the edges in the matching. Then the weight of the Aztec graph A is (A)=  m (m), the ... matching of the graph is a Laurent monomial, and the identities in these monomials combine to give Weyl’s character formula for the representation with highest weight...

Ngày tải lên: 07/08/2014, 08:20

... is the same as the unconditional distribution of ˆy (n) . On the other hand, the conditional distribution of ˆy (n) given that V = n is the distribution of the sequence z (n) under the hypothesis ... initially (0). Then, at each of the n following stages of the BFS, the vertex x at the head of the queue is removed from the queue, and all “new” neighbors of x areadd...

Ngày tải lên: 07/08/2014, 06:22

... L 3 and those edge colorings of K N which are good with respect to these subsets M. We also remark on the connections of these subsets and colorings to projective planes, Ramsey theory, and representations of ... denote the edge between the two vertices x and the electronic journal of combinatorics 15 (2008), #R49 1 Let n ≥ 2 and let E r and E b be as in the proof of lem...

Ngày tải lên: 07/08/2014, 15:23

... 3: The automorphisms of Γ 7 described in the proof of Lemma 3.3.2, for v 7 (left) and v 6 (right). Theorem 3.3.3. The graphs T(Γ 7 ) and O(Γ 7 ) coincide. Furthermore, the graphs T(Γ\Γ 7 ) and ... of Γ 6 . Then x 1 y 1 , x 2 y 2 , x 3 y 3 , x 4 y 4 , x 5 y 5 ∈ {±1}, and their sum is zero if and only if one of these products is not equal to the other four. Thus (x|y) = 0...

Ngày tải lên: 07/08/2014, 21:20

... arguments in terms of the polynomials P n and Q n (Theorem 6.1), and use them together with the computations of §3tofindE n (p/q) for 0 ≤ p ≤ q and q =2,3,4 and 6. We also write the Springer and Shanks numbers ... [17], the numbers c 1,n are just the secant numbers Q 2n (0), and the d 1,n are the tangent numbers P 2n−1 (0). Comparison of the tables in [17] and tho...

Ngày tải lên: 07/08/2014, 06:20

... 8 where P  (x, y)andP  (x, y) are formal power series. The rest of the proof follows the proof of Theorem 3.1.  Another possibility is to analyze the case of permutations containing ... 1)t sin t  , where U j is the jth Chebyshev polynomial of the second kind and cos t =1/2 √ x. 3 Theorem 2.1. The generating function F (x, y; k) for k  1 is given by the con- tinued fra...

Ngày tải lên: 07/08/2014, 06:20

... ≤ √ n .The most likely and the average index of {F(n, d)} are, respectively, the most likely and the average size of the Durfee square of a partition in F(n) and we denote these by m F (n)anda F (n), ... −u 2 g  leads to the equation g  = v. On the other hand, we know that identically e −v + e −g  = 1, and so we conclude that both g  and v are log 2 when G  (x) =...

Ngày tải lên: 07/08/2014, 06:22

... question. Acknowledgments. The authors are grateful to the referees for the careful reading of the manuscript and to M. Atkinson for his remarks. The final version of the paper was written during the first author’s ... S n whose Kazhdan-Lusztig and Poincar´e polynomials, and the singular loci of whose Schubert varieties have fairly simple formulas and descrip- tions. U...

Ngày tải lên: 07/08/2014, 07:21

... to   U k−2  1−x 2 √ x  √ xU k−1  1−x 2 √ x    l 0 −1 (33) and the generating functions for steps 3 and 4 are both equal to (−1) k−2 √ xU k−1  1−x 2 √ x  . (34) Taking the product of x, the quantities in (32) and (33), and the square of the quantity in ... #R7 22 and 2143 and has π(i +1)=n,exactlyoneof1, 2, ,n− i appears to the left of n in π.(Iftwoormoreof1,...

Ngày tải lên: 07/08/2014, 07:21