Báo cáo toán học: "On the number of independent sets in a tree" pdf

... J n q,d is the all one matrix and I n q,d is the identity matrix, both of size n q,d ×n q,d ). Therefore, the largest eigenvalue of V is D q,d and the absolute values of all other eigenvalues are either  (q ... over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors. In this note, we provide a graph theoretic proof of this resu...

Ngày tải lên: 07/08/2014, 15:22

... +1) 6 49n 6 . 7. The number of ascendants of a given node in a LBST As in the case of the number of ascendants in a random BST, computing the probability that the j th node in a random LBST has m ascendants ... solve the differential equations that we had. The last step, that of extracting coefficients in exact form, was, at large, the least system...

Ngày tải lên: 07/08/2014, 06:22

... 6-cycle as in the previous case. Remark: The proof shows that the number of Hamilton cycles is within a poly- nomial factor of the number of two factors of G. Therefore one can generate a (near) random ... segment containing x, the segment containing x  , and the remaining segment. Going round the cycle C i , starting at x  and ending at x, the vertices x,...

Ngày tải lên: 07/08/2014, 06:22

... =2 [Bl]. In the general case, Bender applied a theorem of Hardy, Littlewood and Karamata to the exponential generating function of these permutations to obtain an asymptotic equivalent of the partial ... (single-valued) function in any simply connected domain that avoids its singularities. The lemma shows that the singularity of C m at 1 determines alone the asymptot...

Ngày tải lên: 07/08/2014, 06:23

... points of the planar integer lattice Z 2 , such that for all i<jthe point A i is (weakly) south-east of the point A j , and the point E i is (weakly) south-east of the point E j . Then the number ... 2.3 to obtain a determinant for the number of rhombus tilings. The number of paths from a starting point A i to an end point, which forms an entry in...

Ngày tải lên: 07/08/2014, 08:22

... n for all i. Let a j be the number of rows of R that have exactly j ones. Write a = (a 0 , ,a n )= a( x)inN n+1 .Wenotethat |a| = m,andwrite  m a  for the multinomial coefficient m! a 0 !·· a n ! With ... notation, we have the following lemma. Lemma 6 Let a in N n+1 satisfy |a| = m. Then the number of x in N m such that a( x) =a is  m a  . Let λ =(λ 1...

Ngày tải lên: 07/08/2014, 13:21

... the drawing of the c-graph other than their endpoints. Edges e 1 and e 2 of a c-graph G are parallel if they cross the same edges of G, respectively. That the relation ‘parallel’ is an equivalence relation ... edge, a representative of the set of parallel edges of the e-graph in T . Since, according to Theorem 1, there can be at most two parallel e-graphs, in T...

Ngày tải lên: 07/08/2014, 15:23

... planar map of G in the Euclidean plane. In particular, M has a designated outer (unbounded) face. We denote the sets of vertices, edges and faces of a given planar map by V , E, and F, and their ... encode the 3-coloring on the faces of the central part of ˆ G k, as a sparse sequence a, where a i represents the ith square on the path P indicated by the...

Ngày tải lên: 07/08/2014, 21:20

... consisting of any number of 2  s and 1  s, and its subset of bipartite graphs, we characterize the optimal graphs who maximize and minimize the number of m-matchings. We find the expected value of ... m. In the expression for φ(G, 4) the number of 4-cycles appeared as the first structure in the graph, apart from n and r, which a ects the number of ma...

Ngày tải lên: 07/08/2014, 21:20

...

Ngày tải lên: 05/08/2014, 15:21