Báo cáo toán học: "Operations on Well-Covered Graphs and the Roller-Coaster Conjecture" docx

... e −α/2 ). When the product is expanded, each factor contributes one of either e α/2 or e −α/2 to each term, so that each term in the sum contributes one to the dimension. Hence, the dimension of Ψ ρ is ... in which the vertices are the squares and an edge joins two vertices if and only if the corresponding squares are adjacent in the Aztec diamond. A perfect matching on...

Ngày tải lên: 07/08/2014, 08:20

... 2 operations that preserve well-coveredness under certain conditions may be found in [8], in- cluding the corona, the conjunction, the disjunction, and the Cartesian product of graphs. The case of the ... well-coveredness preserving operations. 2.1 Disjoint Union and the Join Let G 1 and G 2 be well-covered graphs. Then the disjoint union G 1  G 2 is also well- cove...

Ngày tải lên: 07/08/2014, 08:20

... uniform condition-(C) and weak continuous method to obtain uniformly asymptotical compactness in H 1 and H 2 , Yue and Zhong [11] investi- gated the attractors for autonomous and nonautonomous ... f 2 (t )) ∈ Contr(B 0 , ) for the above T.ByLemma2.2andthe property of the functional 〈·,·〉 + a 2 〈∇·, ∇·〉, the conclusion holds. □ Proof of Theorem 2.3 From Lemmas 3.1-3.3, we...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 15:20

... 1994 ABSTRACT Twenty-one years after the publication of A Handbook of Integer Sequences, a greatly expanded version of this collection can now be accessed by electronic mail. 1. The on- line version A Handbook ... 4 Rule 3. The first nontrivial term in the sequence (i.e. the first that exceeds 1) must be less than 1000. The position of the sequence in the lexicographic order in...

Ngày tải lên: 07/08/2014, 06:20

... S 3 acts on itself by conjugation The first proposition follows immediately from the definitions. Proposition 2.1. The group Γ acts on the set X by fixing each element if and only if D Γ (X)=1. The next ... indicated by the numbers within the vertices and the permutation corresponding to each vertex. Let S 4 act on X by conjugation. (This action does consist of graph au...

Ngày tải lên: 07/08/2014, 08:20

... must be the transposition of the remaining two vertices. This implies that the only graphs which have fix(G) = n−1 are the complete graphs and the empty graphs. On the other hand, the graphs with ... of Γ and generate the orbits of vertices of G corresponding to these subgroups using Theorem 2. There are two aspects of this construction which make the procedure d...

Ngày tải lên: 07/08/2014, 21:21

... In Section 3 we give evidence for Conjecture 1.4 and reduce the flag case in Conjecture 1.4 to the inequality for the number of edges. In Section 4 we prove Proposition 1.6 and discuss Conjecture 1.5, ... from the proof of Theorem 1.1(a). Indeed, for a vertex v and a face F ∈ ast(v), (1) and the argument following it imply st(F ) = ast(v) \ lk(v), |F | = r = i, and by induc...

Ngày tải lên: 08/08/2014, 01:20

... used for the proof of Theorem 1.1 do not imply any conclusion when applied to the square peg problem (see Section 4.2). On the other hand, if the square peg problem could be solved for the continuous ... ugh a compar ison of the Serre spectral sequences with Z-coefficients of the Borel constructions associated with the spaces Ω and S(U 4 ×U 2 ) and the subgroup Z 4 = ω...

Ngày tải lên: 08/08/2014, 01:20

... conditional distribution of ˆy (n) given that V = n is the same as the unconditional distribution of ˆy (n) . On the other hand, the conditional distribution of ˆy (n) given that V = n is the distribution of the ... by F n (t)= #{i|1≤i≤nand U i ≤ t} n . We recall a few facts about the convergence of the empirical distribution function towards the distribution function F (t...

Ngày tải lên: 07/08/2014, 06:22