Báo cáo toán học: "Combinatorial interpretations of the Jacobi-Stirling numbers" pot

... be consistent with the model for the Jacobi-Stirling numbers of the first kind. the electronic journal of combinatorics 17 (2010), #R70 4 Combinatorial interpretations of the Jacobi-Stirling numbers Yoann ... 1. The integer LS(n, k) is the number o f signed k-partitions of [±n] 0 . By Theorems 1 and 2, we derive that the integer S(n, k) is the number of signed...

Ngày tải lên: 08/08/2014, 12:22

... dim E, the multiplicity of the irreducible E λ in the c-eigenspace of Λ E r equals the multiplicity of S λ in the c- eigenspace of L |λ|,r . Proof. Suppose |λ| =dimE. Then the c-eigenspace of L |λ|,r is ... to decompose all the eigenspaces of the Laplacian into irreducibles and thereby decompose the homology. They also show that the spectrum of the Laplacia...

Ngày tải lên: 07/08/2014, 06:23

... orbits. In the present case a family is completely specified by the integer q ≡ q 1 which counts the traversals of the loop 1, i.e., the number of letters 1 in the code word. Each of these q letters ... operator u n =trU n (19) as sums of periodic orbits of the graph. The two-point correlations in the spectrum of S (16) can be expressed in terms of the average...

Ngày tải lên: 07/08/2014, 06:23

... hand, the sum of the weights of the perfect matchings of G n is the poly- nomial p n and the sum of the weights of the perfect matchings of H 3 is x 2 1 + x 2 2 + 1, so the sum of the weights of the ... Bijective proof of Lemma 1 The recurrence of Lemma 1 can also be proven bijectively by computing in two different ways the sum of the weights of...

Ngày tải lên: 07/08/2014, 15:22

... g m (ζ)) b a+deg z,∞ a r m {b a+deg z,∞ a r m 1 m 2 qk−p(r) m ρ m } m 1 m 2 qk−p(r) M r [g m ](ζ). (3.11) 11 3. Proof of the results Proof of Theorem 1.4 Suppose that the conclusion of theorem is not true, then there exists an entire solution w(z) satisfies the equation [Q(w(z))] n = ... C, if ζ is not the zero of g(ζ), by (3.4) then we can get g (k) (ζ) = 0 from (3.5). By the...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... in the theory of differential equations and in mathematical physics. Krupka [5] studied the sheaves of differential forms on finite r-jet prolonga- tions J r Y . Then he constructed the sequence of ... 0. 1. Introduction The notion of variational bicomplexes was introduced in studying the problem of characterizing the kernel and image of Euler-Lagrange mapping in the ca...

Ngày tải lên: 06/08/2014, 05:20

... similarly. The proof is complete.  Now we are in a position to proof a version of the well known minimax theorem due to Neumann-Sion [11, 15] in the case of hyperconvex metric spaces. Theorem 3.5. ... Seminar ”Geometry of Banach spaces and Fixed point theory”, organized jointly by the Hanoi Institute of Mathematics and Hanoi University of Education. The author would like...

Ngày tải lên: 06/08/2014, 05:20