Báo cáo toán học: "Comultiplication rules for the double Schur functions and Cauchy identities" docx

... participated in the analysis of the results and drafted the manuscript. AV participated in the analysis of the results and helped to draft the manu- script. AP designed the study, participated in the analysis of ... set [22,23]. The test for molecular clock and esti- mation of the time of split of these two viruses was done with TreePuzzle [21]. Competi...

Ngày tải lên: 19/06/2014, 08:20

... participated in the analysis of the results and drafted the manuscript. AV participated in the analysis of the results and helped to draft the manu- script. AP designed the study, participated in the analysis of ... Access Research Phylogenetic evidence for the distinction of Saaremaa and Dobrava hantaviruses Tarja Sironen, Antti Vaheri and Alexand...

Ngày tải lên: 20/06/2014, 04:20

... q-Bernoulli, q-Euler numbers, and polynomials. 2. q-Bernoulli, q-Euler numbers and polynomials related to the Bosonic and the Fermionic p-adic integral on ℤ p In this section, we provide some basic formulas ... functions of the q-Bernoulli, q-Eule r numbers, and polynomials. We shall provide some basic formulas for the q-Bernoulli and q- Euler polynomials...

Ngày tải lên: 20/06/2014, 21:20

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Ngày tải lên: 05/08/2014, 15:20

... ∈ D 4 (f) then the sequence splits. Proof. Since E ∈ D 4 (f) andL f (α, ) ∈ D 3 (f) (see Proposition 2.11 in [1 ]) then (E,L f (α, )) ∈ S (see Proposition 2.9 in [1 ]). Then by Lemma 1.7 in [1] there ... ν( 2) = max((k, j),m( 2)) . Next we apply ( 4) to k =2,j = ν( 2) and choose ν( 3) = max((k, j),m( 3)) . Continuing this way and by putting a nk = a...

Ngày tải lên: 06/08/2014, 05:20

... several counting problems on the square lattice L n . There the authors gave the following bounds for the asymp- totics of f(n), the number of forests of L n ,and (n), the number of acyclic orienta- tions ... y>0andz t y =1. the electronic journal of combinatorics 10 (2003), #R4 15 Improved bounds for the number of forests and acyclic...

Ngày tải lên: 07/08/2014, 07:21

... of the higher q, t-Catalan sequences. In the rest of the paper, we present some conjectured combinatorial interpretations for the higher q, t-Catalan sequences. We prove some combinatorial formulas, ... proved for these trivariate sequences. 1 Introduction In [7], Garsia and Haiman introduced a q, t-analogue of the Catalan numbers, which they called the q, t-C...

Ngày tải lên: 07/08/2014, 08:22

... in the next section, to prove that a MNT graph of order n ≥ 10 has at least 3n−2 2 edges. The first one concerns the lower bound for the number of edges of MNH graphs. It is the combination of ... is not complete, then some internal vertex of Q has a neighbour in G − V (Q). the electronic journal of combinatorics 12 (2005), #R32 2 Lower Bound for the Size...

Ngày tải lên: 07/08/2014, 13:21

... with n = 7 and s = 27 and get 8k 5 + 15k 6 + 22k 7 + 29  i 8 k i ≤ 58. (8) Multiplication with 3/22 and rounding off yields Lemma 3. the electronic journal of combinatorics 14 (20 07) , #R 27 4 5 ... we show k 3 (7) ≥ 156 and k 3 (8) ≥ 402 improving on the best previously known bounds k 3 (7) ≥ 153 and k 3 (8) ≥ 3 98. The proofs are founded on a recent technique...

Ngày tải lên: 07/08/2014, 15:22

... key ingredient of our proof. Given the informal discussion above, the proof of Theorem 1.1 looks very roughly as follows. At the first part of the proof we consider the graph G(n, ρ) for a relatively ... claim holds for d − 1. We prove the claim for d. Let S = (G 1 , G 2 , . . . , G d ) be the sequence of the labels of the nodes u i , i ∈ [d], along the path...

Ngày tải lên: 07/08/2014, 21:21

... symmetric functions of [21]; cf. formula (3.7) in that paper. Moreover, under the specialization a i = −i + 1 for all i ∈ Z the double Schur functions become the shifted Schur functions of [22] in the variables ... of θ due to the hook formula. Under the specialization a i = i + 1, for any partition à we have a à = (à 1 , à 2 1, . . . ). The following formula f...

Ngày tải lên: 07/08/2014, 21:21

... pair would also form a non-vertical, non-horizontal ℓ-rim hook). Again, | h à (c,b) but h à (a,b) , h à (c,d) . Therefore à cannot be an (ℓ, 0)-JM partition, so λ is not an (ℓ, 0)-JM partition. Conversely, ... if λ is an (ℓ, 0)-JM partition, then S λ = D Rλ . 2 Classifying (ℓ, 0)-JM partitions by their Removable ℓ-Rim Hooks 2.1 Motivation In this section we give a new...

Ngày tải lên: 08/08/2014, 12:22

... such a polygon do not change genus of such a surface. Operation 1: Aaa − ∼ A, Operation 2: AabBab ∼ AcBc, Operation 3: AB ∼ {(Aa), (a − B)}, A A a a A B a b b a A B c c A B A Bc c Figure 4: Operation ... attaching ears serially or by bar -amalgamation of a cactus to G N The authors of [5] discussed a Kuratowski type theorem for average genus of graph...

Ngày tải lên: 08/08/2014, 12:23

... ∞) the electronic journal of combinatorics 17 (2010), #R155 4 A formula for the bivariate map asymptotics constants in terms of the univariate map asymptotics constants Zhicheng Gao ∗ School of ... p g (r) in terms of p g . 1 Introduction The concepts in this paragraph will be made precise in the following paragraphs. The parameters t g and...

Ngày tải lên: 08/08/2014, 12:23

... theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the ... 2}, {15}, the electronic journal of combinatorics 18 (2011), #P60 15 Hybrid Proofs of the q-Binomial Theorem and other identities Dennis Eichhorn Depart...

Ngày tải lên: 08/08/2014, 14:22