Báo cáo toán học: "Colored trees and noncommutative symmetric functions" pdf

... Math. 109 (1993), 557–561. [7] R.FoxandL.Neuwirth,The braid groups, Math. Scand. 10 (1962), 119–126. [8] G.I. Lehrer and L. Solomon, On the action of the symmetric group on the coho- mology of ... combinatorics 4 (1997), #R4 12 [5] P. Edelman and V. Reiner, Free hyperplane arrangements between A n and B n , Math. Z. 215 (1994), 347–365. [6] H Esnault, E. Viehweg, and V. Schechtmann,...

Ngày tải lên: 07/08/2014, 06:20

... n.LetI B and I S be subsets of [k] and let B = {C i : i ∈ I B } and S = {C i : i ∈ I S }. We refer to the sets B and S as the bases and summits of G respectively. A set C i ∈BiscalledabaseofG and ... line, and then we connect n to the lefthand endpoint of the first cycle, the righthand endpoint of each cycle to the lefthand endpoint of the cycle following it, and we connect the...

Ngày tải lên: 07/08/2014, 06:23

... of Panholzer and Prodinger for noncrossing trees and find a correspondence between a class of noncrossing trees, called proper noncrossing trees, and the set of symmetric ternary trees. The second ... 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], Panh...

Ngày tải lên: 07/08/2014, 13:21

... that r ≤ k ([1], [11], [12]) with equality if and only if D ∗ is also affine. When D,D ∗ are both affine then b = v = µm 2 and r = k = µm and D is called a symmetric (µ, m)-net. Note that transversal ... equations in i and j: F ij = α, F  ij = β. There are two cases to examine: Case X = X  :Thenλ>1andsoµ>1. Choose any j (1 ≤ j ≤ µm). Let Y α and Y  β meet the line L j at L j...

Ngày tải lên: 07/08/2014, 06:22

...  i is either (1, 0), (0, 1), or (1, 1), and   i =(p, q). Let h, v,andd be the number of horizontal, vertical, and diagonal steps in L.Thenh + d = p, v + d = q ,and s = h + v + d = p + q − d. The ... have ζ + ◦ T = ζ + and ζ − ◦ T =  (ζ −1 ) −  −1 . (57) Proof. Both S and T are antimorphism of coalgebras and morphisms of algebras QSym → QSym. In addition, ζ ◦S = ζ −1 and ζ ◦T...

Ngày tải lên: 07/08/2014, 08:22

... G[X] and G[X] are critical, 2-connected and non-bipartite, and that |F ∩ EG[X]| ≡ |X| − 1 2 (mod 2) for all 1-factors F . Then the unique brick resulting from the decomposition of G into bricks and ... passes through x. Let e and f be the edges of C incident on x. Let u and v, respectively, be the ends of these edges in X. Let M e and M f be perfect matchings of G containing e...

Ngày tải lên: 07/08/2014, 15:22

... Michael Saks, and Vera T. S´os, Maximum induced trees in graphs, J. Combin. Theory Ser. B 41 (1986), no. 1, 61–79. [3] Wenceslas Fernandez de la Vega, Induced trees in sparse random graphs, Graphs ... “bipartite” and with f T replaced by f B . Proof: We let W = {w 0 , . . ., w m−1 }, and write r = m − 1 and q = t − 1 to simplify expressions. As G is triangle-free it follows that t...

Ngày tải lên: 07/08/2014, 15:23

... L. W. Shapiro, A bijection between ordered trees and 2-Motzkin paths and its many consequences, Discrete Math. 256 (2002), 655–670. [9] R. Donaghey and L. W. Shapiro, Motzkin numbers, J. Combin. ... Panayotopoulos and A. Sapounakis, On Motzkin words and noncrossing partitions, Ars Combin. 69 (2003), 109–116. [16] J. Riordan, Combinatorial Identities, John Wiley and Sons, 1968. [...

Ngày tải lên: 07/08/2014, 08:22

... Computational Linguistics Dependency trees and the strong generative capacity of CCG Alexander Koller Saarland University Saarbrücken, Germany koller@mmci.uni-saarland.de Marco Kuhlmann Uppsala University Uppsala, ... these de- pendency trees to compare the strong gen- erative capacities of CCG and TAG and obtain surprising results: Both formalisms generate the same languages of der...

Ngày tải lên: 31/03/2014, 20:20

... 3 This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. The structural and optical properties ... measurements, and drafted the manuscript. CY conducted the STEM measurement. SZ, TH, and GH conducted the MBE growth. JH, WW, and CH coordinated the study. WL provided the idea...

Ngày tải lên: 20/06/2014, 20:20