Báo cáo toán học: "Generating function for K-restricted jagged partitions" pot

... realization of the K-restricted jagged partitions for K odd has been found recently, in the context of superconformal minimal models [14]. 2 Jagged partitions Let us start by formalizing and exemplifying ... λ j = λ j+1 = λ j+K−2 + K − 1=λ j+K−1 + K − 1 . (63) To transform a generating function for K-restricted jagged partitions to one for partitions subject to (62) and (63)...

Ngày tải lên: 07/08/2014, 08:22

... and deg g d (z). In Theorem 1 we showed that the generating function for V (d, n) is a rational function f d (z)/g d (z). Theorem 2. For all d  1 we have deg f d (z)  deg g d (z) − 2d. (2) Proof. ... as before, but now with a 5×5 ma trix. Also gcd(det(K), det(I −T z)) = 1 in this case. The diagram in Fig. 2 shows the walk for the permutation (3142) by using the “erase”-process fo...

Ngày tải lên: 08/08/2014, 01:20

... involving ribbon Schur functions which will be used to derive our expression for F L S (x, Q, P). In section 4, we shall give our method for finding the g enerating function for F L S (x, Q, P) and ... (3.2) yields (3.1). 4 Methods for Computin g Generating Functions In this section, we shall describe how we can use ribbon Schur functions to compute various generating functions over...

Ngày tải lên: 08/08/2014, 12:22

... computing |G(n)| up to n = 1000 should be feasible. For a related counting problem, we note that Stanley [St] has obtained a generating function for f(n), the number of sequences (x 1 ,x 2 , ,x n ) ... π  2 − 1, α i = π i+1 − 1 for 1 ≤ i ≤ m and α  i = π  i+1 − 1for1 ≤ i ≤ d(π) − 1. Clearly, f is a bijection between P  (n, k, l)and P(n −k − l +1,k−1,l−1) Furthermore, for 1 ≤ j ≤...

Ngày tải lên: 07/08/2014, 06:20

... red K m,m or a green K n,n . We obtain asymptotic bounds for b (m, n ) for m ≥ 2 fixed and n → ∞. 1 Introduction Recent exact results for bipartite Ramsey numbers [4] have rekindled interest in ... by T is green. Then P (R S ) = p m 2 for each of the  r m  2 choices of S, and we simply write P(R) for the common value. In the same way, P(G) = (1 − p) n 2 for each of  r n  2 poss...

Ngày tải lên: 07/08/2014, 06:22

... not a weak ℓ-partition for 0 < k < ϕ − 1, 4. e k i λ is not a weak ℓ-partition for 1 < k < ε. 4.2 Crystal theoretic results for ladd ℓ and (ℓ, 0)-JM partitions For a proof of these ... in λ for k  b can be at most h (c,b) ℓ = d−b+a−c+1 ℓ < 2(d−b)+1 ℓ < d − b since ℓ > 2. In order for (c, d) to be a n addable position, we need to have exactly d − b boxes (c,...

Ngày tải lên: 08/08/2014, 12:22

... the Jacobi–Trudi identity we transform the original determinant identity into an equivalent identity for Schur functions, • Third, we obtain a bijective proof for this equivalent identity by using ... P. Goulden , Quadratic Forms of Skew Schur Functions, European J. of Combi- natorics, 9 (1988), 161–168 [8] A. Hamel, private communication, 1997. [9] C.G.J. Jacobi, De formatione et proprie...

Ngày tải lên: 07/08/2014, 06:22

... Bailey- Borwein-Bradley’s identities for generating functions of the sequences {ζ(2n+2)} n≥0 and {ζ(2n + 3)} n≥0 . By the same method, we give several new representations for these generating functions yielding ... yielding faster convergent series for values of the Riemann zeta function. 1 Introduction The Riemann zeta function is defined by the series ζ(s) = ∞  n=1 1 n s , for R...

Ngày tải lên: 07/08/2014, 15:23

... that each of them has the form (−1) m−k− 1 e k (u)p − m−k (u − k), and the Newton’s formula for elementary symmetric functions e m (u, τ) follows. The proof for homogeneous functions is similar. the ... RTT equation for the Yangian. It is inspired by the paper [2] on Newton’s identities for RTT algebras with R-matrices that satisfy Hecke type condition. Proposition 4. (Newton’s formul...

Ngày tải lên: 08/08/2014, 01:20

... distributed freely for any purposes (see copyright notice below). For information about publishing your research in EURASIP WCN go to http://jwcn.eurasipjournals.com/authors/instructions/ For information ... netbooks. All this need for flexibility and more “mobile” devices lead to more and more needs to afford the spectral resources that shall be able to satisfy costumers need for mo...

Ngày tải lên: 20/06/2014, 20:20