Báo cáo toán học: "An entropy proof of the Kahn-Lov´sz theorem a" ppsx

... A proof of the Kahn-Lov´asz theorem The entropy proof of the Kahn-Lov´asz theorem is complicated by the fact that there can be edges of the graph (and a fixed matching) amongst the neighbors of ...  E is independent of the event {x  V y}. Proof. For any permutation of the edges of m, there is a permutation of V (G) inducing it. Therefore, the unif...

Ngày tải lên: 08/08/2014, 12:23

... (5) The proof of (3) is completely combinatorial, the proof of (4) uses nothing more than the fundamental theorem of algebra, and the proof of (5) is a simple geometric argument. Proof of (3). The ... hooks in the diagram of λ. Many proofs of this fact have been given, of varying complexity. We present here an elementary new proof which uses nothing mor...

Ngày tải lên: 07/08/2014, 15:23

... regular words (that is, elements of W M k ) 0-variable words, then the Hales-Jewett theorem corresponds to the case n =0,t = 1 of Theorem 1.4. Theorem 1.4 Let k, r, n, t ∈ N be given. There exists M = M(k, ... θ,as required. In our application of Theorem 2.8, we shall not utilize idempotence of φ. Theorem 2.9 (See [FK, Theorem 2.1]. Also [HS, Theorem 2.23] or [M1, T...

Ngày tải lên: 07/08/2014, 06:20

... depends on the ratio of interelement spacing of the array to the wavelength. In the case that the angle ambiguity occurs, we refer to [14-16] for resolving the ambiguity. The remainder of this article ... it is believable that the number of the selected principle components i n step (b) of Table 2 is equal to the num- ber of the actual sources ; for lower SNR...

Ngày tải lên: 20/06/2014, 20:20

... replace the o(n −7/2 ) error term in the asymptotic expansion of B(n)/n!withO(n −9/2 ln 19 n). The following extension of Theorem 1 (the case m = 3) giving a complete asymptotic expansion of I(n, ... example) that the b(n, k) satisfy a central limit theorem with µ n =  n 2  /2andσ 2 n = n(n − 1)(2n +5)/72 (see [2; Theorem 1]). Bender [2; p. 109] remarks that the theore...

Ngày tải lên: 07/08/2014, 06:20

... A D be the adjacency matrix of Γ D .IfA D belongs to the algebra generated by A, then A D = J −R(A), where R := r 2 P − r 2 +1 and P is the alternating polynomial of Γ. P roof. The first part of the ... 1), which concludes the proof of the theorem. ✷ For general k, the given bound (3 ) is sharp. For instance, in [14] it was shown that the alternating polynomial P (...

Ngày tải lên: 07/08/2014, 06:22

... H(G) does not exceed the number of connected components of its low-vertex subgraph L(G). Proof of Theorem 1. Let L(G) and H(G) be the low-vertex and the high-vertex subgraphs of G, respectively. ... ingredient of our proof is the following result of Stiebitz. Lemma 3 ([5]) Let G be a k-critical graph containing at least one vertex of degree k − 1. Then the number...

Ngày tải lên: 07/08/2014, 06:22

... electronic journal of combinatorics 10 (2003), #R39 8 2.3 Proof of Theorem 1.5 Before proceeding to the proof of Theorem 1.5, we begin by describing the constants involved, the setup we use and ... our proof of Theorem 1.5, we do not appeal to the matrix argument of Section 1.1.2. We show G  2 =⇒ G 1 follows directly from an application of the Szemer´edi Reg...

Ngày tải lên: 07/08/2014, 08:20

... when the first author was visiting the Department of Mathematical Sciences of the University of Delaware, and when the second author was visiting the Department of Mathematics of the University of ... this is the case, and the proof of our lemma is finished.  Remark The end of the proof above requires ∆ ≤ n/4 + 1. One may wonder why then in the stateme...

Ngày tải lên: 07/08/2014, 21:21

... ends the proof of Case 2, and of Theorem 1.  Acknowledgment The authors are thankful to Sebastian Cioab˘a, Gary Ebert, and Qing Xiang for their comments on the original version of our proof. ... in a graph with more that t r (n − 1) edges, and the proof of the theorem will easily follow. Let u i be a vertex in A with the lowest degree. Then d(u i ) ≤ 1 r + 1 r+1...

Ngày tải lên: 08/08/2014, 12:23