Báo cáo toán học: "Linear Discrepancy of Basic Totally Unimodular Matrices" pptx

... investigate the linear discrepancy of strongly unimodular 0, 1 matrices. One part of their work is devoted to the case of basic strongly unimodular 0, 1 matrices, i. e. strongly unimodular 0, 1 matrices ... Primary 11K38 Abstract We show that the linear discrepancy of a basic totally unimodular matrix A ∈ R m×n is at most 1 − 1 n+1 . This extends a result of Peng a...

Ngày tải lên: 07/08/2014, 06:20

... ν},whereS 3 is some subset of m  − 1elementsofS 0 ∪ S 1 and T 3 is some subset of n  − 1elementsofT 0 ∪ T 1 . From the previous section we know that the determinant of this transformation is ... →∞through integer multiples of m/t. Proof. The theorem is an example of an Edgeworth expansion. We need the case of multivariable lattice distributions, such as Corollary 22.3 of [3]....

Ngày tải lên: 07/08/2014, 13:21

... x of F 3 induces a valuation f x : F 1 → N; y → d(x, y) − d(x, F 1 )ofF 1 . So, we can distinguish the points of F 3 by means of the type of valuation of F 1 they induce. From this point of ... 5.6.7]. An SDPS-set of a dual polar space of rank 0 consists of the unique point of that dual polar space. An SDPS-set of a thick generalized quadrangle Q is an ovoid of Q. For...

Ngày tải lên: 07/08/2014, 13:21

... formed by reversing the order of the rows of M. As for the matrix P of 3.1.3(2), we have seen above that it is the integral encoding of the rectification S of any tableau T of which M is the integral ... the number of squares of row i that the picture f maps to row k, while Bin(f) k,j counts the number of squares of column j that f maps to row k. From the form of part b i...

Ngày tải lên: 07/08/2014, 13:21

... face vectors of 2-dimensional Buchsbaum simplicial complexes. We recall the basics of simplicial complexes. A simplicial complex ∆ on [n] = {1, 2, . . . , n} is a collection of subsets of [n] satisfying ... Betti numbers of ∆ (over K). The link of ∆ with respect to F ∈ ∆ is the simplicial complex lk ∆ (F ) = {G ⊂ [n] \F : G ∪F ∈ ∆}. In the study of face vectors of simplicial c...

Ngày tải lên: 07/08/2014, 21:21

... the set of its grid-quads. The automorphism group of G n , n  4, has two orbits on the set of grid-quads of G n , namely the set of grid- quads of Type I and the set of gr id-quads of Type II. Every ... vector of weight 2 of V . If M is a big max of G n , n  3, then  M ∼ = G n−1 . Suppose M is a big max of G n corresponding to a vector ¯x of weight 2 of V . The...

Ngày tải lên: 08/08/2014, 01:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 09:46

... that the assertion of Theorem 2.2 remains valid if instead of (c1)–(c4) we use (c1)–(c5). The method of dealing with (c5) is similar to that of dealing with (c4) in the proof of Theorem 2.2. Up ... verification of (4) is reduced to the problem of finding z ∈ U x and μ J ∈ R |J| such that (12) holds. Here |J| denotes the number of elements in J. We substitute z from the first equa...

Ngày tải lên: 06/08/2014, 05:20

... either multiples of b in [1, z 0 ] or not divisible by b. This implies that |B| ≤ |A n | and completes the proof of part (i) of Theorem 3.1. Proof of Part (ii) : We divide the proof into two cases. Case ... contains no multiples of b. But then another application of the induction hypothesis yields that |B| ≤ |A  n | in this case too. Thus part (ii) of the theorem is proved. Pro...

Ngày tải lên: 07/08/2014, 15:23