Báo cáo toán học: "MacMahon-type Identities for Signed Even Permutations" docx
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 IntroductionA classic theorem by MacMahon ... qi−1+2qi).5 Even -signed Even PermutationsWe denote by Dnthe group of even -signed permutations, that is the subgroup of Bnconsisting of all the signed permutations having an even number of ... factor and a signless even factor.In [3], Biagioli proved an analogue of MacMahon’s theorem for the group of even -signed permutations Dn (signed permutations with an even number of sign changes)....
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Báo cáo toán học: "Distinguishing numbers for graphs and groups" docx
... associated to a fixed group. In other words,given a group Γ we ask for the setDΓ= {k : k = D(G) for a graph G with Aut(G)=Γ}. For instance, the wreath product S2[S3] is the automorphism group ... {y1, ,yj} satisfies1. φ(yi)=i for each i,2. yi+1is in Γi−1.yi for each i from 2 to j − 1, and y1is in Γj−1.yj,then j ≤ m and |Γi−1.yi|≥j − i + 2for each i from 2 to j.Proof. ... of Construction 2.7. If {y1, ,yj} is a subset of X such that1. φ(yi)=i for each i,2. yi+1is in Γi−1.yi for each i from 2 to j − 1, and y1is in Γj−1.yj,then |Γ|≥|Γ1.y2||Γ2.y3|···|Γj−1.yj||Γj.y1||StabΓj(y1)|.the...
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Báo cáo toán học: "Bijective proofs for Schur function identities which imply Dodgson’s condensation formula and Pl¨cker u relations" pps
... combinatorics8 (2001), #R16 8[4] M. Fulmek and C. Krattenthaler, Lattice path proofs for determinant formu-las for symplectic and orthogonal characters, J. Combinatorial Theory A77(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, Desnanot proved it for n≤6 ... Figure 2 for an illustration), and where the weightw(P) of such an r-tuple P is defined as before.4 Bijective proof of Theorem 2Proof: Let us start with a combinatorial description for the...
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Báo cáo toán học: "Automated Proofs for Some Stirling Number Identities" pptx
... 6With the recurrence for F (m, n) at hand, it is an easy matter to prove the closed formrepresentationF (m, n) =12(n + 1)(n + 2)S1(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 S1and the obvious relations for factorials,harmonic numbers, etc. it is ... available. Therefore, g(m, n, k) (the only informa-tion contained in (5) but not in (6)) is called the certificate of the recurrence.In the following section, we give a detailed example for proving...
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Báo cáo toán học: "Comultiplication rules for the double Schur functions and Cauchy identities" docx
... provide explicit formulas for the images of the double elementary andcomplete symmetric functions hm(x||a) and em(x||a) with respect to the comultiplication∆.Another formula for the dual Littlewood–Richardson ... G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford UniversityPress, Oxford, 1995.[16] L. C. Mihalcea, Giambelli formulae for the equivariant quantum cohomology of theGrassmannian, ... sµ(x/y||a),implied by the combinatorial formula (2.14). Therefore, the required relation follows bycomparing the two expansions.An explicit formula for the polynomials cνλµ(a) is provided...
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Báo cáo toán học: "Elementary Proofs for Convolution Identities of Abel and Hagen–Rothe" pps
... cn. (2)These convolution identities are fundamental in enumerative combinatorics. The readercan refer to Strehl [15] for a historical note. The existing proofs for the identities of Abeland Hagen–Rothe ... journal of combinatorics 17 (2010), #N24 3 For the identities displayed in (1) and (2) , their linear combinations yield the fo llowingrespective symmetric formsnk=0aa + bk(a + bk)kk!c ... knowledge, there does not seem to have appeared really elementary proofs for these identities in classical combinatorics, even though this has long been desirable.By utilizing the standard method...
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Báo cáo toán học: " Spectrum sensing for cognitive radio exploiting spectrum discontinuities detection" potx
... distributed freely for any purposes (see copyright notice below). For information about publishing your research in EURASIP WCN go tohttp://jwcn.eurasipjournals.com/authors/instructions/ For information ... netbooks. All this need for flexibilityand more “mobile” devices lead to more and more needs to afford the spectral resourcesthat shall be able to satisfy costumers need for mobility. But, as ... We clearly see that for the proposed technique, the higher the order, the more performing the detector gets.6. ConclusionIn this article, we presented a new standpoint for spectrum sensing...
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Báo cáo toán học: " Resource reservation for mobile hotspots in vehicular environments with cellular/WLAN interworking" ppt
... distributed freely for any purposes (see copyright notice below). For information about publishing your research in EURASIP WCN go tohttp://jwcn.eurasipjournals.com/authors/instructions/ For information ... delay.According to the performance evaluation, we can derive the required channel bandwidth for such a mobilehotspot. Numerical results are presented to demonstrate the application for bandwidth reservation, ... 1: System parameters for numerical analysisSymbol Value Definitionα 1.3484 Parameter of sigmoid function for video classificationβ 5.2924 Parameter of sigmoid function for video classificationδ...
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Báo cáo toán học: " Resource Allocation for Asymmetric Multi-Way Relay Communication over Orthogonal Channels" potx
... Fig. 3. It can be7closed 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 tohttp://jwcn.eurasipjournals.com/authors/instructions/ For information ... transformed into a linearoptimization problem that is solvable with computa-tionally efficient algorithms. Moreover, we obtain aclosed form expression for the rate optimization thatis valid for...
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Báo cáo toán học: " Decision making for cognitive radio equipment: analysis of the first 10 years of exploration" potx
... distributed freely for any purposes (see copyright notice below). For information about publishing your research in EURASIP WCN go tohttp://jwcn.eurasipjournals.com/authors/instructions/ For information ... todayFigure 725decision making architectures for CR. We notice however, that except the one designed by Mitola, duringthe DARPA xG Program, and those designed and implemented by Virginia Tech, the ... [14,34,61]. GAs were first designed to mimic Darwin’s evolution-ary theory and are well known for their capacity to adapt themselves to a changing environment. Withoutusing our formalism, their study...
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