Báo cáo toán học: "Discrepancy of Matrices of Zeros and Ones" docx

... G ∗ ∼ = P D+1 and for some k ∈ [2, D − 1], the vertices u ∗ k−1 and u ∗ k+1 of G ∗ are both not of type (1). Then u ∗ k−1 and u ∗ k+1 are both of type (N). Proof. Let x and y be twins of u k−1 and u k+1 respectively. ... of type (1) are adjacent, and one of them is a leaf of type (K), then the other is also of type (K). Proof. As illustrated in Figure 12, le t x a...

Ngày tải lên: 08/08/2014, 12:22

... from which Corollary 1 follows. ✷ Discrepancy of Matrices of Zeros and Ones Richard A. Brualdi ∗ and Jian Shen † Department of Mathematics University of Wisconsin Madison, Wisconsin 53706 brualdi@math.wisc.edu ... each i =1, 2, and 2. The intersection of each row of A with region i is connected for each i =1, 2, and define, for each A ∈A(R, S), the discrepancy d(A)ofA t...

Ngày tải lên: 07/08/2014, 06:20

... properties of nonnegative matrices and their permanents, Soviet Math. Dokl. 14:945-949 (1973). [4] R. A. Brualdi, J. L. Goldwasser and T. S. Michael, Maximum permanents of matrices of zeroes and ones, ... moments, (6).  Maximising the permanent of (0,1) -matrices and the number of extensions of Latin rectangles B. D. McKay and I. M. Wanless Department of Computer...

Ngày tải lên: 07/08/2014, 06:22

... ∈ X d ,sof is a bijection. For all x ∈ X d \ D the f–orbit O f (x)ofx has order 2 and consists of x and f(x). Further we have {x i |i ∈ [d]} = {f(x) i |i ∈ [d]}, the electronic journal of combinat ... fixed d. Our proof of the lower bound is a variation of the Fourier transform method (in the literature also called circle–method). The novelty of our proof is the application of...

Ngày tải lên: 07/08/2014, 08:20

... polynomial in x and y of degree ≤ deg f +1. By induction and (4) it follows that the coefficients of G are rational numbers. This proves the lemma. 5 End of the proof Since G is a polynomial of degree ... electronic journal of combinatorics 13 (2006), #N8 5 3 Start of the proof Let N = {0, 1, }. Define the weight of a matrix N to be the sum of its entries, and write |N| for...

Ngày tải lên: 07/08/2014, 13:21

... point of X either red or blue, in such a way that any of the sets of F has roughly the same number of red points and blue points. The maximum deviation from an even splitting, over all sets of F, ... elements of X as x 1 ,x 2 , ,x n and the sets of F as S 1 ,S 2 , ,S m in some arbitrary order. The incidence matrix of (X, F)isthem × n matrix A, with columns corresponding to...

Ngày tải lên: 07/08/2014, 13:21

... used in the proofs of Theorem 8 and Theorem 10 are different. References [1] J. Beck and V. T. S´os, Discrepancy theory, in R. Graham, M. Gr¨otschel, and L. Lov´asz, Editors, Handbook of Combinatorics, ... respect to χ. Proof of Lemma 7. The proof is based on an argument from Ramsey theory. First we verify the statement of Lemma 7 for a fixed simplex. Then, by induction over the n...

Ngày tải lên: 07/08/2014, 13:21

... recall the definition of the density matrices of a graph and define the tensor product of three graphs, reconsider the tripartite entanglement properties of the density matrices of graphs introduced ... for separability of density matrices of nearest point graphs and perfect the electronic journal of combinatorics 14 (2007), #R40 1 where I n and J n is the n ×n ident...

Ngày tải lên: 07/08/2014, 15:22

... then fo llows from Theorem 3 and ess sup 0x1 |g(x)| = D ∗ N (P). 3.5 The proof of Theorem 5 Proof. We go back to our definition of D P N as the expected value of the random variable     # {x i : ... The proof of Theorem 4 Proof. We start with the lower bound. Taking a random interval could be simulated as follows: we start by t aking any random point α in [0, 1] and then take...

Ngày tải lên: 08/08/2014, 12:22

... analysis, and writing of the manuscript. AW and SJ participated in the conception and design of the study and revised the manuscript for important intellectual content. All authors read and approved ... Watcharapasorn 1,2 , and Sukanda Jiansirisomboon* 1,2 1 Department of Physics and Materials Science, Faculty of Science, Chiang Mai University, Chiang Mai, 50200,...

Ngày tải lên: 20/06/2014, 20:20