Báo cáo toán học: "Continued fractions and Catalan problems" pot

... result follows from the previous theorem and Theorem 1. References [1] Tofik Mansour and Alek Vainshtein, Restricted permutations, continued fractions and chebyshev polynomials, The Electronic ... 4 2 Lattice paths and ordered trees We draw our ordered trees with the root at the top and proceed downward to the leaves. The first leaf is the leftmost leaf in the drawing and the rema...

Ngày tải lên: 07/08/2014, 06:20

... = sin q (u) cos q (u) generalises for w = q r the Foata and Han version, and for w = −1 the Cieslinski version. Our elementary approach can handle this situation as well: Set σ 0 (z) =  n≥0 (w; ... and q-cotangent functions. Discrete Math. Theor. Comput. Sci., 12(2):47–64, 2010. the electronic journal of combinatorics 18(2) (2011), #P18 7 Continued fractions related to (t, q)-tangent...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 10:20

... explicit determination of root systems and lattices involved. 5 Acknowledgements We thank Ed Assmus, Michel Deza, and Vladimir Tonchev for sending us their preprints and Chris Charnes, Slava Grishukhin ... paper R9. J.H. Conway , N.J.A. Sloane, Sphere Packings Lattices and Groups [SPLAG] J.H. Conway, N.J.A. Sloane, Sphere Packings Lattices and Groups, second edition, Springer Verlag...

Ngày tải lên: 07/08/2014, 06:20

... (1995), 313–316. [12] West, J. Generating trees and the Catalan and Schr¨oder numbers. Discrete Math. 146 (1995), 247–262. [13] West, J. Generating trees and forbidden subsequences. Proceedings of ... the two trees, and therefore a unique bijection between tournament sequences and Meeussen sequences which respects the ideas of extending or truncating a sequence. To better understa...

Ngày tải lên: 07/08/2014, 06:20

... J. Riordan, Mappings of acyclic and parking functions, ae- quationes math. 10 (1974), 10–22. [9] A. M. Garsia and M. Haiman, A remarkable q, t -Catalan sequence and q-Lagrange inversion, J. Algebraic ... poset of rank n with ˆ 0and ˆ 1 and with rank function ρ. (See [29, Ch. 3] for poset terminology and notation used here.) Let S be a subset of [n − 1] = {1, 2, ,n−1}, and define...

Ngày tải lên: 07/08/2014, 06:22

... |X|≥k. Note that the minpaths and mincuts of (E,φ)are the k-subsets and (n − k + 1)-subsets of E, respectively. Now, let E be totally ordered, and for k-subsets X and Y of E define X  Y :⇔ x ≤ ... network and φ(X) = 1 if and only if X contains the edges of an s, t-path. For source-to-T -terminal reliability we take Σ = (E,φ), where E is the edge-set of the network and φ(X)=1 if...

Ngày tải lên: 07/08/2014, 06:22

... transposing theentries 0and1 atindices 1and2 of(µ + α)[ ] or by transposing the entries −2 and −3 at indices 3 and 4. The result can be written as (4, 3, 3, 2, 2)[ ] respectively as (4, 2, 4, 1, 3)[ ], and indeed ... Corollary. For λ, µ ∈Pand α ∈C, the Kostka number K λ/µ,α equals the number # SST(λ/µ, α) of semistandard tableaux of shape λ/µ and weight α ,and K  λ/µ,α is the number...

Ngày tải lên: 07/08/2014, 08:22

... within the circle and do not cross each other. Noncrossing trees have been studied by Deutsch, Feretic and Noy [2], Deutsch and Noy [3], Flajolet and Noy [4], Noy [6], Panholzer and Prodinger [7]. ... ··· ,C r and C  1 ,C  2 , ··· ,C  r are the cycles encountered in the edge deletion procedures for T and T  .Since(i 1 ,i 2 ) /∈ E(T ), we may assume that (i 1 ,i 2 ) ∈ E(C j )...

Ngày tải lên: 07/08/2014, 13:21

... ∪ . VB(K) and the edges are partitioned E(K) = EW(K) ∪ . EG(K) ∪ . EB(K). The sets VW and VB are the white and black vertices, respectively, and the sets EW, EG and EB are the white, gray and black ... of graphs. The theorems of Erd˝os and Stone [15] and Erd˝os and Simonovits [14] give that d ∗ (M) = 1/r, where r = min{χ(F ) − 1 : F ∈ M} and p ∗ (M) = 1. Alon and Stav,...

Ngày tải lên: 07/08/2014, 15:23