Báo cáo toán học: "A normalization formula for the Jack polynomials in superspace and an identity on partitions" pps

... b i in P [k] j,i . the electronic journal of combinatorics 16 (2009), #R70 18 A normalization formula for the Jack polynomials in superspace and an identity on partitions Luc Lapointe ∗ Instituto ... where σ j and ∂ j are respectively the interchang e and divided difference operators on the variables a j and a j+1 (see for instance [6]). The main ste...

Ngày tải lên: 07/08/2014, 21:21

... performs on P operation (α), and one application of operations (β) and (γ) for any cell in c n . ii. P satisfies U2 (and not U1). The operator ϑ performs on P operation (δ), and one application ... of P (see for instance, Figure 4). Reentrant and salient points were considered in [12], and successively in [9], in a more general context, and it was proved that in...

Ngày tải lên: 07/08/2014, 15:22

Ngày tải lên: 05/08/2014, 15:20

... below them in both T and T  . Order the k −1’s by placing the k −1’s in row r first and other k −1’s later. The algorithm for determining m k−1 (T ) and m k−1 (T  ) give the same result. Finally, ... functions and complete symmetric functions. In Section 1, some tableaux and symmetric function notation is given. In Section 2, the work of [D] is reviewed. The k...

Ngày tải lên: 07/08/2014, 06:20

... Acknowledgment The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The author also thanks Prof. Cheng Zhao for his advice. References [1] J.A. Bondy and U.S.R. Murty, Graph Theory ... denote the number of vertices, and (G) denote the number of edges. In this paper, we construct a graph G having no two cycles with the same length which leads t...

Ngày tải lên: 07/08/2014, 06:22

... balanced if and only if e(i)=e(j) for all i, j. In [11], Wagner and West conjectured that exponentially balanced Gray codes exist for all length n. By extending the method of Robinson and Cohn for ... (2005), #N19 5 with the formulation in [4] are due to our convention with respect to the labelling of bit positions and the indexing of codewords as introduced in Sec...

Ngày tải lên: 07/08/2014, 08:22

... k − 1) and λ = (k + 1, . . . , k + 1    k−1 , k, k). Note that no k-deletion of µ can contain the cell (k, k + 1) and that no k-deletion of λ can contain the cell (k + 1, k). Therefore every ... whether and where r and c intersect. the electronic journal of combinatorics 15 (2008), #N23 2 Case 3: r and c do not intersect. Suppose that the rightmost cell in row r is (r,...

Ngày tải lên: 07/08/2014, 15:22

... Everest and Thomas Ward, Heights of polynomials and entropy in alge- braic dynamics, Universitext, Springer-Verlag London Ltd., London, 1999. [Leh85] D. H. Lehmer, Interesting series involving the ... expressions for the Gromov norm of a knot complement. In this note we show that those formulae yield interesting power series expansions for the logarithm function. This gene...

Ngày tải lên: 07/08/2014, 15:23

... suffices. Acknowledgments The author thanks Herbert Wilf and Janet Beissinger, who was the first to explore [1] combinatorial proofs using colored permutations, for their assistance. References [1] Janet Beissinger. ... that (π, f) = φ((π, f )) if and only if R (π,f) = ∅, or if and o nly if κ(π) = n (so π = e n , the identity permutation of S n ) and f : K π → A is injective. T...

Ngày tải lên: 08/08/2014, 01:20

... in the various worldwide pharmacopeias and in Section 21 of the Code of Federal Regulations (CFR), International Conference on Harmonisation (ICH) and Food and Drug Administration Points to Consider ... medicinal products. In particular the European Regulation makes reference to and is in coherence with the 2004/23/EC directive on donation, procurement and testin...

Ngày tải lên: 18/06/2014, 15:20