Báo cáo toán học: "Generalized Cauchy identities, trees and multidimensional Brownian motions Part I: bijective proof of generalized Cauchy identities ´ Piotr Sniady" pot

... work [ ´ Sni03] where we provided the first proof the electronic journal of combinatorics 13 (2006), #R62 10 Generalized Cauchy identities, trees and multidimensional Brownian motions. Part I: bijective ... and entropy. American Mathematical Society, Providence, RI, 2000. [J ´ S06a] Artur Je˙zandPiotr ´ Sniady. Generalized cauchy identities, tree...

Ngày tải lên: 07/08/2014, 13:21

... Drmota and Gittenberger derived asymptotics of all moments (without rate) of width of general simple trees. In [7], the results of Subsections 4.3 and 4.5 are generalized to study the “emergence of ... theta-distributed random variables occur as a limit for the height of trees: see R´enyi and Szekeres (1967) for rooted labeled trees, Flajolet and Odlyzko (1982) for g...

Ngày tải lên: 07/08/2014, 06:22

... between trees with an even and an odd number of descents D(z,−1) and symmetric ternary trees[ 1]. Question 4.2. Find a bijection on trees with 2k + 1 edges between those with k − 1 descents and those ... number of edges, d(τ)isthenumber of descents, and a(τ ) is the number of ascents. A butterfly is an ordered pair of subtrees T and T ∗ that lie on either side of an...

Ngày tải lên: 07/08/2014, 07:21

... odd(λ). 3 Combinatorial Proofs of Theorems 1.1, 1.2, and 1.3 In this section, we give combinatorial proofs of the q-binomial theorem and Theorems 1.2 and 1.3. Our combinatorial proof of the q-binomial ... and n. The purpose of this paper is to give combinatorial proofs of (1.1), (1.2), and (1.3) by using conjugation of 2-modular diagrams. As usual, a partition λ is defi...

Ngày tải lên: 07/08/2014, 07:21

... Mahmoud and R. Smythe, On the distribution of leaves in rooted subtrees of recursive trees, Annals of Applied Probability 1, 406–418, 1991. [6] H. Mahmoud and R. Smythe, A Survey of Recursive Trees, ... recursive trees and binary increasing trees. We study the quantity number of descendants of node j in a random tree of size n and give closed formulæ for the probabi...

Ngày tải lên: 07/08/2014, 13:21

... families of trees will be determined precisely such as when T k is a broom, double star, and subdivided star. The class of trees for which sat(n, T k ) < n will be explored, and large classes of trees ... two vertices of high degree, say u and v, and all neighbors of u and v (other than u and v) are end vertices. Thus, by adding the edge between x ∈ N(u) − v an...

Ngày tải lên: 08/08/2014, 01:20

... r-skeleton, and by Theorem 1.1(b), for any 1 ≤ j ≤ r, f j (∆) ≥  f 0 (S(i,d)) j+1  ≥ f j (S(i, d)). Proof of Theorem 1.1(d). This follows from the proof of Theorem 1.1(a). Indeed, for a vertex v and ... , A proof of the lower bound co njecture for convex polytopes, Pacific J. Math. 46 (1973), 349–354. MR MR0328773 (48 #7115) [4] Louis J. Billera and Carl W. Lee, A proof...

Ngày tải lên: 08/08/2014, 01:20

... very short proofs of our main results – Theorems 4, 5, 6 and 7. 2 Embedding trees in expanding graphs We start by defining a class of expanding graphs that seems t o be most adequate and convenient ... almost spanning bounded degree trees. The most technical (but standard) parts Sections 3 and 4, are entirely devoted to the study of expansion properties of random graphs and...

Ngày tải lên: 08/08/2014, 11:20

... electric and magnetic poten- tial barrier on the surface of a 3D topological insulator, as shown in Figure 1. We can create magnetic and electric potentials underneath a superconducting plate and ... spin of the charge carriers, while for graphene it stands for the pseudo spin, i.e., the A and B sublattices of graphene. Hence, it is natural to manipulate spin transport on the su...

Ngày tải lên: 20/06/2014, 20:20

... hoc, and wireless-sensor networks can be configured to sup- port localization functionality. Indoor environments, however, are particularly challenging because of severe multipath and non-line -of- sight ... design of efficient positioning systems. The objective of this special issue, which was pro- moted under the auspices of the EC Network of Excel- lence in Wireless Communica...

Ngày tải lên: 20/06/2014, 21:20