Báo cáo toán học: " The Redheffer matrix of a partially ordered se" doc

... dominant eigenvalues, and showed that the eigenvalues that are neither dominant nor equal to 1 are o((log n) 2/5 ). Added in proof: our evaluation of the permanent of the original matrix of Redheffer, ... literature In a general partially ordered set, Richard Stanley [9] has introduced a matrix that is closely related to ours. Indeed, take the Redheffer matrix R(S...

Ngày tải lên: 07/08/2014, 08:22

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Ngày tải lên: 05/08/2014, 10:20

... further that any subgroup L of G/N has the property that D(L) ≤ c. Then D(G) ≤ c +1. Proof. The case G = 1 is trivial. Suppose that a nontrivial group G acts faithfully on a set X.ChooseasetU of ... given a nonfaithful action of G on X, we may consider instead the faithful action of the quotient group G/Stab(X) on X,whereStab(X) denotes the elements of G that fix each...

Ngày tải lên: 07/08/2014, 13:21

... of a dense random graph. The notion of a t-stable set is a generalisation of the notion of a stable set. Recall that a set of vertices S of a graph G is stable if no two of its vertices are adjacent. ... are adjacent. In other words, the maximum degree of G[S] is 0, and therefore a stable set is a 0-stable set. The study of the order of the larg...

Ngày tải lên: 08/08/2014, 12:22

... USAP, and all the main procedures of the latter (except for the principal SAWUmSc) have the name of their USAP counterparts, with a “W” attached. For example, FollowersW is the SAW-adaptation of ... installment of the five-part saga on the Umbral Transfer -Matrix method, based on Gian-Carlo Rota’s seminal notion of the umbra. In this article we describe the Maple...

Ngày tải lên: 07/08/2014, 06:22

... inequalities (1) imply the Galois identities eae = e and aea = a, by e ≤ e(ae) = (ea)e ≤ e, and a ≤ (ae )a = a( ea) ≤ a. As we shall see however, the Galois identities are only the first pair in a list of identities that ... h(e n 1 ). This list of numbers is unimodal. The suffix peaks are the increasing ter ms at the right of the sequence, while the prefix peaks ar...

Ngày tải lên: 08/08/2014, 14:23

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Ngày tải lên: 05/08/2014, 15:20

... discuss a special M -matrix linear system, when the matrix A in linear system (1) is a diagonally dominant L -matrix; this matrix class often appears in input-output model and finite Markov chain (e.g., ... the fact that each principal submatrix of a nonsingular M -matrix is also a nonsingular M -matrix, we know that Theorem 2.4 and Corollary 2.5 extend Theorem 1.1. Refer...

Ngày tải lên: 06/08/2014, 05:20

... sequence of transformations. That is, we seek the antecedents of the final polyomino obtained at the end of the sequence of transformations. The main idea is that we started the sequence of transformations ... by 23 the number of horizontal contacts is maximal after application of p 3 . Moreover the number of vertical contacts between two adjacent columns is als...

Ngày tải lên: 07/08/2014, 06:20

... drawing of G,theplanar subdivision of G is the graph obtained by adding vertices (and corresponding adjacencies) at each of the edge crossings of the particular drawing of G. Is the planar subdivision ... ν(K n )=ν(K n ) then the convex hull of any optimal rectilinear drawing of K n is a triangle. Prove that the convex hull of any optimal rectilinear drawing of...

Ngày tải lên: 07/08/2014, 06:22