Báo cáo toán học: "MacMahon-type Identities for Signed Even Permutations" docx

... We prove analogues of MacMahon’s equidistribution theorem for the group of signed even permutations and for its subgroup of even -signed even permutations. 1 Introduction A classic theorem by MacMahon ... q i−1 +2q i ). 5 Even -signed Even Permutations We denote by D n the group of even -signed permutations, that is the subgroup of B n consisting of all the signed permu...

Ngày tải lên: 07/08/2014, 08:22

... associated to a fixed group. In other words, given a group Γ we ask for the set D Γ = {k : k = D(G) for a graph G with Aut(G)=Γ}. For instance, the wreath product S 2 [S 3 ] is the automorphism group ... {y 1 , ,y j } satisfies 1. φ(y i )=i for each i, 2. y i+1 is in Γ i−1 .y i for each i from 2 to j − 1, and y 1 is in Γ j−1 .y j , then j ≤ m and |Γ i−1 .y i |≥j − i + 2for each i fro...

Ngày tải lên: 07/08/2014, 08:20

... combinatorics 8 (2001), #R16 8 [4] M. Fulmek and C. Krattenthaler , Lattice path proofs for determinant formu- las for symplectic and orthogonal characters, J. Combinatorial Theory A 77 (1997), 3–50. [5] W. ... condensation formula [2], which is also known as Desnanot–Jacobi’s adjoint matrix theorem (see [1, Theorem 3.12]: According to [1], Lagrange discovered this theorem for n = 3, De...

Ngày tải lên: 07/08/2014, 06:22

... 6 With the recurrence for F (m, n) at hand, it is an easy matter to prove the closed form representation F (m, n) = 1 2 (n + 1)(n + 2)S 1 (m, n + 2). Just check that the closed form satisfies the ... g(m, n, k) allows us to verify the recurrence for F (m, n) independently. Indeed, using the triangular recurrence (1) for S 1 and the obvious relations for factorials, harmonic numbers, et...

Ngày tải lên: 07/08/2014, 15:22

... provide explicit formulas for the images of the double elementary and complete symmetric functions h m (x||a) and e m (x||a) with respect to the comultiplication ∆. Another formula for the dual Littlewood–Richardson ... G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford, 1995. [16] L. C. Mihalcea, Giambelli formulae for the equivariant quantum cohomo...

Ngày tải lên: 07/08/2014, 21:21

... c n  . (2) These convolution identities are fundamental in enumerative combinatorics. The reader can refer to Strehl [15] for a historical note. The existing proofs for the identities of Abel and Hagen–Rothe ... journal of combinatorics 17 (2010), #N24 3 For the identities displayed in (1) and (2) , their linear combinations yield the fo llowing respective symmetric forms n  k=0...

Ngày tải lên: 08/08/2014, 11:20

... 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

... 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 ... delay. According to the performance evaluation, we can derive the required channel bandwidth for such a mobile hotspot. Numerical results are presented to demonstrate the applicat...

Ngày tải lên: 20/06/2014, 20:20

... Fig. 3. It can be 7 closed form expressions for the optimal time allo- cation. We also obtained a closed form expression for the optimal rate allocation that is valid for spe- cific channel conditions ... 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/instruc...

Ngày tải lên: 20/06/2014, 20:20

... 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 ... today Figure 7 25 decision making architectures for CR. We notice however, that except the one designed by Mitola, during the DARPA xG Program, and those designed and implemented...

Ngày tải lên: 20/06/2014, 20:20