Báo cáo toán học: "Rook Theory, Generalized Stirling Numbers and (p, q)-analogues" docx

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

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Ngày tải lên: 05/08/2014, 15:20

... on generalized convolu- tion, for instance: the generalized convolution for integral transforms Stieltjes, Hilbert and the cosine- sine transforms [12], the generalized convolution for H- transform ... γ(y)=sign y for the Fourier, Fourier cosine and sine transforms of functions f and g has a meaning and belongs to L(R) and the factorization...

Ngày tải lên: 06/08/2014, 05:20

... d j    = G  . COMBINATORIAL PROOFS OF CAPELLI’S AND TURNBULL’S IDENTITIES FROM CLASSICAL INVARIANT THEORY BY Dominique FOATA ∗ and Doron ZEILBERGER ∗∗ 0. Introduction. Capelli’s [C] identity ... Kostant and Sahi [K-S] discovered and proved an anti-symmetric analog of Capelli’s identity. Although we, at present, are unable to give a combinatorial proof si...

Ngày tải lên: 07/08/2014, 06:20

... that the graph Γ i is the i-th class of the scheme, and so we indistinctly use the words graph or “class” to mean the same thing. 2 The Proper and Adjacency Polynomials In this section we introduce ... trivial.) Then, by the converse of Theorem 2.5 , it must be Q k  u ≥ 1. On the other hand, in the proof of Theorem the electronic journal of combi...

Ngày tải lên: 07/08/2014, 06:20

... harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multi- variate ... this section, we deal with an abstract graph G satisfying certain conditions listed below. In the next sections, concrete examples of G will be considered. Our assumptions...

Ngày tải lên: 07/08/2014, 06:20

... is to construct parametrically new symmetric designs and non- embeddable quasi-residual designs. The main tool in both constructions are balanced generalized weighing matrices. A balanced generalized ... (1963), pp. 399–402. the electronic journal of combinatorics 8 (2001), #R12 15 Applying balanced generalized weighing matrices to construct block designs Yury J...

Ngày tải lên: 07/08/2014, 06:22

... family of generalized (p, q) -Stirling numbers which includes our (p, q) -Stirling numbers s i,j n,k (p, q)andS i,j n,k (p, q) can be found in [19] where the authors interpret generalized (p, q) -Stirling ... recursions. c i,j 0,0 (p, q)= 1and c i,j n,k (p, q)=0ifk<0ork>n (29) and c i,j n+1,k (p, q)=c i,j n,k−1 (p, q)+[i + nj] p,q c i,j...

Ngày tải lên: 07/08/2014, 08:22

... 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...

Ngày tải lên: 07/08/2014, 13:21

... regarding the moments and limiting distribution of the individual entries of a random unitary matrix. The matrix U k is called the kth truncation of U. Truncations of random unitary matri- ces have ... express the moments of Tr(U k ) in terms of the Weingarten function as follows: the electronic journal of combinatorics 14 (2007), #R21 6 Truncations of Random Uni...

Ngày tải lên: 07/08/2014, 15:22

... cardinality is a metric basis of G, and |S| is the metric dimension of G, denoted by β(G). For positive integers β and D, let G β,D be the class of connected graphs with metric dimension β and diameter ... Extremal Graph Theory for Metric Dimension and Diameter ∗ Carmen Hernando † Departament de Matem`atica Aplicada I Universitat Polit`ecnica de Catalunya Barcelona...

Ngày tải lên: 08/08/2014, 12:22

... a l ). 4 Convexity lemma In this section we give a short polynomial proof of the convexity lemma, which is the crucial step in S´a-Thompson theorem [7, 10]. The original proofs of S´a and Thompson were ... elementary but very long and does not involve the concept of convexity. Later on shorter, combinatorial proof was given in [8]. Here we give the first purely polynomial pr...

Ngày tải lên: 08/08/2014, 12:22