Báo cáo toán học: "Maximum exponent of boolean circulant matrices with constant number of nonzero entries in their generating vector" docx

... the nonzero entries in the generating vector of C. Then, for k ≥ 1, kS is the set of positions of the non zero entries in the generating vector of C k . Proof. The proof is by induction on k. If ... constant number of nonzero entries in their generating vector. We also give matrices attaining such exponents. Solving this problem we also solve two equiva...

Ngày tải lên: 07/08/2014, 21:21

... single variable instance of the exponential formula.) In this case, A(x, y)=e yC(x) is the generating function for structures by number of components and is an ordinary generating function in ... remainder of the proof is nearly the same as that for (a), with (i − k)θ modulo 2π in place of θ k . Proof (of Theorem 5): We begin by deriving the description of Λ h .LetS b...

Ngày tải lên: 07/08/2014, 06:20

... every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. Let G be a connected graph of order n with minimum degree ... attaching a copy of H to a vertex v in a graph G we mean adding a copy of H to the graph G and joining v with an edge to the link vertex of H. We call v an attached...

Ngày tải lên: 07/08/2014, 15:23

... k-sum-free subset of {1, 2, ,n} one takes the integers within the three intervals ob- tained by multiplying each real number in S 3 (3, 1) by n (with slight modi- fication of the end-points due to integer ... contradiction. Finding the value of u 2 =sup{x ∈ S | x< 2 k } is the key point in determining the structure of S; u 2 will turn out to be the right end-point of the se...

Ngày tải lên: 07/08/2014, 06:20

... K. Proof. By Lemma 24 and since k has a finite number of components, there exists a K such that every component of k contains an edge for all k ≥ K. By Lemma 14, M k is a subset of the components in k .Thus,M k contains ... support of his Honors Thesis, of which this work is a part. We also thank the referees for their suggestions. References [1] R. L. Hemminger and L. W. Beine...

Ngày tải lên: 07/08/2014, 06:20

... The set of incidence vectors of the matchings of G have a convex hull which is equal to the polytope containing all x ∈ R E which satisfy the following the electronic journal of combinatorics ... graphs with fixed d ≥ 3, the fraction of unmatched vertices in a maximum matching is exponentially small in the girth of the graph. For 2- regular graphs (which is to say, collection...

Ngày tải lên: 07/08/2014, 13:21

... C 5 was determined in a celebrated paper of Lov´asz [5]. For a survey of zero-error information theory see [4]. The problem of determining the independence numbers of arbitrary products of odd cycles remains ... maximum independent in C d k2 d +1 . Note that, since the intersection of S with any 2-dimensional slice projects onto a maximum independent set in C 2 k2 d +1 , w...

Ngày tải lên: 07/08/2014, 21:21

... an endpoint of P n . Then P n \v consists of two disjoint paths, say Q 1 and Q 2 . Let u 1 be the endpoint of Q 1 such that it is a neighbor of v in P n . Consider the paths Q 1 and Q 1 v in P n . Since ... maximum multiplicity of a root of the matching polynomial of a tree to be equal to the minimum number of vertex disjoint paths needed to cover it. 1 Introduction All...

Ngày tải lên: 07/08/2014, 21:21

... determining the extreme points; (2) interpolating the extreme points for the mean envelope; and (3) subtracti ng the signal using the mean envelope. Determining the extreme points and the interpolation ... discussed in the following section. The window of openness is 5-15 pixels in different itera- tions. Both the threshold of the minimal points fo r posi- tive openness and threshold...

Ngày tải lên: 20/06/2014, 20:20

... RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea Full list of author information is available at the end of the article Abstract Shrinking projection algorithms for finding ... [1-8]). In [9], Takah ashi and Zembayashi proved strong and weak converge nce theorems for finding a common element of the set of solutions of an equilibrium problem and the set of...

Ngày tải lên: 20/06/2014, 21:20