Báo cáo toán học: "Proof of an intersection theorem via graph homomorphisms" docx

... homomorphism, ¯α(H n ) ≥ ¯α(H) for any graph H. We now can present the proof of the theorem. Proof: Firstnotethatifp =1/2thenµ p is the uniform measure and the theorem is trivial because if a vector in ... measure on G n our theorem now translates precisely to the statement ¯α(G n ) ≤ p. the electronic journal of combinatorics 13 (2006), #N6 2 Proof of an intersection theor...

Ngày tải lên: 07/08/2014, 13:21

... into an infinite sequence of consecutive intervals I 0 ,I 1 , ANALYSIS OF AN ASYMMETRIC LEADER ELECTION ALGORITHM Svante Janson Wojciech Szpankowski ∗ Department of Mathematics Department of Computer ... asymptotics of the mean and the variance of the height. The next Theorem 2 provides an asymptotic expression for the distribution of the height. We close this section wi...

Ngày tải lên: 07/08/2014, 06:20

... p). (4) Proof.Let G={(σ, σ, τ):σ, τ ∈ S p , 0τ =0}. (5) G acts on FDLS(p). By Lemma 3, sgn(Lg)=sgn(L) for any L of order p and any g ∈ G.LetRbe any set of representatives of the orbits of G in FDLS(p), ... journal of combinatorics 5 (1998) #R28 3 the G-isotopy class of L.TheG-autotopism group G (L)ofLis the stabilizer of L in G. Clearly |G| = |LG|| G (L)| (3) for any G< n and...

Ngày tải lên: 07/08/2014, 06:22

... According to Theorems 1 and 4, Φ a,b,c is a polynomial of total degree ab+bc+ca, and a symmetric polynomial of the {α i } of degree at most a in each, of the {β i } of degree at most b in each, and of ... of symmetry under interchange of spectral parameters The purpose of this appendix is to provide an explicit proof of the symmetry of the partition function of weigh...

Ngày tải lên: 07/08/2014, 13:21

... purpose of the present note to try to lay bare the basic mechanism of Kouba’s proof. 2 Proof of Theorem 2 The proof of the Theorem 2 will be based on the following simple lemma. Lemma 3. Let R be an ... change in the setting of integral domains. the electronic journal of combinatorics 17 (2010), #N14 3 Proof of Theorem 2. Let R be an arbitrary integral domain and f ∈ R...

Ngày tải lên: 08/08/2014, 11:20

... e(T ), then T ⊂ G. Furthermore, for any x ∈ U 1 and any a ∈ X, we can map x → a; alternatively, for any leaf y ∈ ˜ U 2 and any b ∈ Y , we can map y → b. Proof of Lemma 7.4 for trees with at least ... n. This general Theorem 3.3 is necessary for the proof of Theorem 1.9 and becomes useful if one wants to show that G ⊃ T n under a (slightly) smaller value of ℓ(G). Proof of Theorem...

Ngày tải lên: 08/08/2014, 12:23

... claimed. 3 Asymptotic expansion It remains to prove Theorem 1 and obtain an asymptotic expansion for t n = s n /(n!) 2 .Itis possible that this can be done with a careful analysis of the series f S (Π 0 )=  Π µ(Π)g S (Π) since ... series E(X):= ∞  n=0 n!X n and T (X):= ∞  n=1 n!t n X n . Then Section 2 of [5] shows that E(X)=expT (X)andso T (X)=logE(X). (1) We shall apply a theore...

Ngày tải lên: 07/08/2014, 13:21

... certain standard and semistandard Young tableaux. We combine our formula with a variant of the Colour-Flavour Transformation of lattice gauge theory to give a combinatorial expansion of an interesting ... Colour-Flavour Transformation of lattice gauge theory to give another formulation of Theorem 1, which gives a combinatorial expansion for an interesting type of matrix inte...

Ngày tải lên: 07/08/2014, 15:22

... number of right-to-left minima i of σ satisfying σ −1 (N + 1) < i. Proof. This just means that in (5) we can replace the statistic u with u ′ , and this can be done via a simple bijection. For any ... point of view by exchanging the empty sites with occupied sites. It can also be obtained from the Matrix Ansatz by using the transposed matrices D ∗ and E ∗ and the transposed vectors...

Ngày tải lên: 08/08/2014, 12:23

... such graph of order n contains a cycle of length Ω(log h(a,t) n). 1 Introduction In this paper, all graphs are finite and simple. A graph H is a minor of a graph K if H can be obtained from a subgraph ... existence of k-trees and the toughness of a graph, Graphs Combin. 5 (1989) 201–205. the electronic journal of combinatorics 18 (2011), #P148 6 Toughness of K a,t -minor-...

Ngày tải lên: 08/08/2014, 14:23