Báo cáo toán học: " Large convexly independent subsets of Minkowski sums" ppt

... the largest k such that for each m there the electronic journal of combinatorics 17 (2010), #R146 5 Large convexly independent subsets of Minkowski sums Konrad J. Swanepoel ∗ Department of Mathematics London ... 3-dimensional case of this function. 4.1 Convexly independent subsets of Minkowski sums in 3-space Theorem 6. ⌊ 1 3 n 2 ⌋  E 3 (n)  3 8 n 2 + O(n 3/2 )....

Ngày tải lên: 08/08/2014, 12:23

... entirely devoted to the study of expansion properties of random graphs and graphs with large spectral gap. Finally, in Section 5, based on this study, we give very short proofs of our main results – ... n, provided that T has at least λn leaves. 3 Expanding properties of random graphs For two not necessarily disjoint subsets of the set of vertices of a graph G, let e(A, B) :...

Ngày tải lên: 08/08/2014, 11:20

...

Ngày tải lên: 05/08/2014, 10:20

... ⊆ ker(α) = 0, and so M is projective, as required. The proof of (5) ⇒ (1) is similar to that of (7) ⇒ (2) in Theorem 3.7. (7) ⇒ (1). By the proof of Proposition 2.3, every P -injective right R-module is ... semisimple Artinian. By a slight modification of the proof of [21, Theorem 2], we obtain the following Proposition 3.10. Let X b e a non-empty subset of a ring R. The following...

Ngày tải lên: 06/08/2014, 05:20

... be a p-subgroup of G (l) . Then the fixed point set of H has the structure of a regular linear space with lines of size k.Hence|Fix(H)|≥k 2 − k +1. Proof: From the conditions of the lemma it is ... Systems. The choice of notation was determined by the use of the language of linear spaces by a number of authors as well as the need to study the fixed points of automorphisms. S...

Ngày tải lên: 07/08/2014, 06:20

... coverings of the integers given the m k ) and minimize the a’s and b’s con- structed by Knuth’s method. Thus the minimum values of a and b are determined for the pairs (p k ,m k ). 2 Proof of Regularity Before ... consist of only composite terms. 6 Thanks My thanks to Richard Guy [3] and Paulo Ribenboim [5, 6] for pointing out this problem in their books, and the makers of PARI [1]...

Ngày tải lên: 07/08/2014, 06:20

... cardinality of the largest set of nodes X ⊂ T such that T ≤x  ∼ = T ≤y whenever x, y ∈ X with x = y. In other words, λ(T) is the minimum number of labels needed for T.Notethatify is a descendant of ... that agrees with s n (Q) for all large n. the electronic journal of combinatorics 9(2) (2003), #R6 16 There are only six symmetry classes of two element subsets of S 3 , lis...

Ngày tải lên: 07/08/2014, 07:21

... number of appearances of i as a part of π. The parts of π  in non-increasing order are thus N  i=1 f i (π), N  i=2 f i (π), N  i=3 f i (π), , N  i=N f i (π). (11) Note that some of the entries ... z,y −1 ). (15) Proof. We shall in the following be dealing with partitions whose parts are all  some given N.Welet¯π be that partition made up of the parts of π that are <N. I...

Ngày tải lên: 07/08/2014, 08:22

... number of the action of G on X, denoted D G (X), is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a color- preserving permutation of ... number of the action of G on X, denoted D G (X), is the smallest r admitting a distinguishing r-coloring of X with respect to the action of G. If there does not exist a distin...

Ngày tải lên: 07/08/2014, 13:21

... elements of −1. The trace of (Λ 2 A) ⊤ (Λ 2 A) is the sum of squares of the singular values of Λ 2 A, which equals (σ 1 (Λ 2 A)) 2 = σ 2 1 σ 2 2 in our case. This trace also equals the sum of squares ... Introduction The purpose of this paper is to study the maximum value of the maximum eigenvalue of certain classes of bipartite graphs. These problems are analogous to the...

Ngày tải lên: 07/08/2014, 21:21