Báo cáo toán học: "An Infinite Antichain of Permutations" ppsx

... partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain. In other words, there exists an infinite collection of permutations no one of which contains ... usually much more complex than permutations. 2 The infinite antichain We are going to construct an infinite antichain, {a i }. The elements of this antichain will be very...

Ngày tải lên: 07/08/2014, 06:20

... design in the infinite family has the collection of five blocks mentioned above then so do all other members of the infinite family; 3) Give a design having the required collection of five blocks. Theorem ... matrix ofa2-(v, k, λ)designisab × v matrix A = a ij ,in which a ij =1ifblocki contains point j and a ij =0otherwise. 3 Results The strategy for establishing the existence of an...

Ngày tải lên: 07/08/2014, 06:20

... derivative of Z X (u) is a generating function for the number of circuits. See for instance [7]. Knowing the number of circuits of each length is sufficient to conclude the number of primitive circuits of ... demonstrate add itional families of pairs of graphs which share the same zeta function. 1. Introduction In 2009 , Cooper described an infinite family of non-isomorphic p...

Ngày tải lên: 08/08/2014, 12:22

... structural properties and that the natural way to describe the structure of these graphs is in terms of graph homomorphisms. One infinite sequence of cores of dense maximal triangle-free graphs was known. All graphs ... 4-colourable, in contrast to a conjecture of Jin [8], saying that there are graphs of arbitrarily large chromatic number with this property. Another infinite seq...

Ngày tải lên: 07/08/2014, 06:22

... construct new infinite families of 3-designs. 1 Introduction A t − (v, k, λ) design is a pair (X, B) where X is a v-element set of points and B is a collection of k-element subsets of X called blocks, ... derive the order of D + f from the number of solutions of y 2 = f(x). In particular, when y 2 = f(x) is in a certain class of elliptic curves, there is an explicit formula f...

Ngày tải lên: 07/08/2014, 15:22

... accumulation vertices of degree 6. Proof. Figure 6 illustrates a construction of a plane graph F 1 that fulfills all conditions of the definition of a plane 13-belt graph except (B1). Splitting of a vertex ... communication and preprint of [2]) that typi- cal constructions of infinite families of simple 3-connected k-crossing-critical graphs create bounded numbers (wrt. k) of...

Ngày tải lên: 07/08/2014, 21:20

... B T C  , where A is of size m × m, B is of size m × (n − m) and C is of size (n − m) × (n − m). The sizes of blocks are shown on the margins of the matrix. Let s denote the number of 1’s in B. Then ... elements of π are the last 3 elements of σ, i.e. 5 4 2. The middle part of π is the electronic journal of combinatorics 14 (2007), #R2 8 9 8 7. The first part of π is the...

Ngày tải lên: 07/08/2014, 15:22

... prefix of x of length 5. Proof. Firstnotethatthewordyis necessarily overlap-free by assertion 1 of Lemma 2. The existence of the decomposition for finite words is proved in [10], in the proof of Theorem ... this factorization of x,thewordu(resp. v) depends only on the prefix (resp. suffix) of x of length 7. This is recalled in the following table of all possible prefixes (resp. su...

Ngày tải lên: 07/08/2014, 06:22

... a tree. Proof: It suffices to prove that every edge of T (G) is an isthmus. Corollary 9 shows that if [x, y] is any hinge of G, then the cleavage units of G are precisely the cleavage units of the ... of K,oneofH and J is 2-connected. It is straightforward to show the corresponding one of H  and J  is also 2-connected, so that (H  ,J  ) is a hinge-separation of G. But then eve...

Ngày tải lên: 07/08/2014, 08:20

... the infinite hypercube Q of dimension is defined as the Cartesian product of copies of K 2 . Its vertex set is the set of all functions of a set S of cardinality into {0, 1}, where the preimage of ... an infinite graph of bounded, finite degree and G contains a one-way infinite isometric path R. Let u 0 be the first vertex of R, and label all vertices of R with ∆, where ∆...

Ngày tải lên: 07/08/2014, 15:22