Báo cáo toán học: "Discrepancy of Symmetric Products of Hypergraphs" pdf

... behavior of the coefficients of large powers of multivariate generating functions and their application to mul- tivariate Lagrange inversion. In Theorem 2 of [5] we studied coefficients of large powers of ... our theorem for products of powers. In Section 3 we explain how the theorem applies to Lagrange inversion of a single function and discuss the problem of conditioning on...

Ngày tải lên: 07/08/2014, 06:20

... dimension d and the number of colors, whether the discrepancy of symmetric products is more like the discrepancy of the original hypergraph or the d-th power thereof. Let us make this precise: Let ... 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 numbe...

Ngày tải lên: 07/08/2014, 13:21

... introduced in the beginning of this article: We have disc(G, 2) = 2 disc(G). the electronic journal of combinat orics 11 (2004), #R5 8 Discrepancy of Cartesian Products of Arithmetic Progressions Benjamin ... determine the combinatorial discrepancy of the hypergraph H of cartesian products of d arithmetic progressions in the [N] d –lattice ([N ]={0, 1, ,N − 1}). The study o...

Ngày tải lên: 07/08/2014, 08:20

... for short) of two terms of each binomial is 1. Denote by x p the g.c.d. of the first term of f u and the first term of f v , by x t the g.c.d. of the first term of f u and the second term of f v , ... primary decomposition of the presentation ideal of the Symmetric algebra Sym(I) in Theorem 3.1. All these results are independent of the characteristic and of the cardinal...

Ngày tải lên: 06/08/2014, 05:20

... journal of combinatorics 6 (1999), #R15 9 the column sum vector of C 1 .ThusC = C 2 ∈J. This contradicts the choice of C. ✷ Theorem 2 |U| = |V |. Proof. Let D =(d ij ). By the choice of D,wehave|U|≤|V ... completes the proof of the lemma. ✷ Suppose S is monotone. For each A ∈A(R, S), we can partition A into two regions according to the shape of ¯ A; that is, region 1 consists of...

Ngày tải lên: 07/08/2014, 06:20

... 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, ... Discrepancy of Sums of Three Arithmetic Progressions AleˇsPˇr´ıvˇetiv´y ∗ Department of Applied Mathematics of Charles University Malostransk´en´am. 25, 11800 ... [MS96]. Discre...

Ngày tải lên: 07/08/2014, 13:21

... S n for the symmetric group of permutations of [n]. For any finite set I, let Π(I) denote the poset of partitions of the set I, where a partition π of I is a set of nonempty disjoint subsets of I whose ... d [1]). (4.17) the electronic journal of combinatorics 13 (2006), #R87 19 of (conjugate) parabolic subsystems of a root system of type B n all of whose components a...

Ngày tải lên: 07/08/2014, 13:21

... an orientation of a gra ph G is a directed graph O with the same vertices, so that for every edge {i, j} of G, exactly one of (i, j) and (j, i) is an edge of O. An orientation is often regarded ... < j ℓ . The subring of Q[[x 1 , x 2 , . . .]] consisting of all quasisymmetric functions will be denoted Q, and the vector space spanned by all quasisymmetric functions of degree n...

Ngày tải lên: 08/08/2014, 12:23

... average number of reached nodes— it is a sort of approximated indicator of the “depth” of the propagation process. Since the RE can be interpreted as the ratio between the average number of reached ... conditions— this is the very idea of IF. The shape of p, as a function of d, is shown in Figure 5, for different values of c and ρ s . It can be observed that the PAF of SIF...

Ngày tải lên: 20/06/2014, 20:20

... the large amount of cadmium-containing waste during the deposi- tion process. Therefore, the development of a Cd-free buffer layer is one of the major objectives in the field of CIGS solar cells. Today, ... 7:26 http://www.nanoscalereslett.com/content/7/1/26 Page 7 of 7 The influence of the substrate temperatures on the sur- face morphology of the films was investigated using th...

Ngày tải lên: 20/06/2014, 21:20