Báo cáo toán học: " Canonical characters on quasi-symmetric functions and bivariate Catalan numbers" pot

... −→ Q Sym F σ −→ F D(σ) (46) the electronic journal of combinatorics 11(2) (2005), #R15 24 Canonical characters on quasi-symmetric functions and bivariate Catalan numbers ∗ Marcelo Aguiar Department ... E˘gecio˘glu and Alastair King, Random walks and Catalan factorization,Pro- ceedings of the Thirtieth Southeastern International Conference on Combinatorics, Graph Theor...

Ngày tải lên: 07/08/2014, 08:22

... ad- dress configuration time ( ¯ T conf ), by simply consider- ing the two possible configuration situations: (i) there is on average multi-hop connectivity between the un- configured vehicle and the ... evaluated the config- uration time ¯ T conf under different traffic conditions and for different deployment configuration parame- ters. The traffic conditions are defined by the vehicu- lar density...

Ngày tải lên: 20/06/2014, 20:20

... Decomposition Lemma, E 1 and E 2 partition {1, ,n−1}. Set S 1 =(s i :i∈E 1 ),S 2 =(s i :i∈E 2 )−s ∗ n . By part 3 of the Decomposition Lemma, S 1 and S 2 are major sequences of length l − 1andn−l, ... Recursively obtain the trees T 1 = f(S 1 )andT 2 =f(S 2 )on{ 0, ,l−1} and {0, ,n−l} respectively, with e(T 1 )=a(S 1 )ande(T 2 )=a(S 2 ), and thus by Part 4 of the Decomposition Lemma e...

Ngày tải lên: 07/08/2014, 06:22

... L ∈ Σ P k .Above, the notation · , · refers to some canonical pairing function. With these definitions, NP = Σ P 1 ,coNP=Π P 1 ,andtheclassesΣ P k and Π P k form a neat hierarchy containing P and lying inside ... the definition of AM. Based on constructions like those of [12, 10, 11], one has AM ⊂ Σ P 2 ∩ Π P 2 ,com- pleting the claim in the introduction. One naturally wonders at the...

Ngày tải lên: 07/08/2014, 06:22

... A note on odd cycle-complete graph Ramsey numbers Benny Sudakov ∗ Department of Mathematics, Princeton University, Princeton, NJ 08544, USA and Institute for Advanced Study, Princeton, NJ 08540, ... vertex v contains no 2k-vertex path. On the other hand it is well known that the graph with minimal degree 2k contains such a path. Therefore any induced subgraph of G[N(v)] should contain v...

Ngày tải lên: 07/08/2014, 06:23

... b ′ . 2.2 Rigged configurations A general definition of rigged configuration of arbitrary types can be found in [14, Section 3.1]. Here we are only concerned with type A n rigged configurations and review ... pr on RC and conjectured [14, Conjecture 4.12] that pr corresponds to the promotion operator pr under the bijection Φ. Several necessary conditions of promotion operators were establis...

Ngày tải lên: 08/08/2014, 12:22

... Joynt and Coppersmith in [7], Douglas and Wang in [1], and Gamble, Friesen, Zhou and Joynt in [4] use the idea of evolving a quantum walk on a given pair of graphs and then comparing a permutation-inva ... Simone Severini, and Richard C. Wilson. A matrix representation of graphs and its spectrum as a graph invariant. Electr. J. Comb., 13(1), 20 06. [3] David Emms, Simone Sever...

Ngày tải lên: 08/08/2014, 14:23

... function,” in Continued Fractions and Orthogonal Functions: Theory and Applications, ed. S. Clement Cooper and W. J. Thron, M. Dekker, 1994, pp. 233–279. [19] W. H. Mills, D. P. Robbins, and H. Rumsey, ... York, 1974. [13] W. B. Jones and W. J. Thron, Continued Fractions: Analytic Theory and Applications, En- cyclopedia of Mathematics and Its Applications, Vol. 11, Addison-Wesl...

Ngày tải lên: 07/08/2014, 06:20

... With the initial condition, this recursion uniquely determines the multivariable generating functions C n,k (by induction on n and backwards induction on k). To prove this recursion, we classify ... constructed from D  therefore belongs to case 3. Consider the definition (35) with D replaced by D  and k replaced by k + 1. If we substitute w = 0 in that definition (with the usual con...

Ngày tải lên: 07/08/2014, 08:22

... The Kronecker product of symmetric group representations, J. London Math. Soc. 31 , 1956, 89-93. [Ma] I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford U. press, second edition, ... ions 3.1 and 3.4 when α and β are partitions of the same number and from equation 3.9 when they are not. This given, 2) follows by linearity from equation 3.2. Finally, 3) follows from equ...

Ngày tải lên: 08/08/2014, 01:20