Báo cáo toán học: "New infinite families of 3-designs from algebraic curves of higher genus over finite fields" potx

... New infinite families of 3-designs from algebraic curves of higher genus over finite fields Byeong-Kweon Oh ∗ Department of Applied Mathematics Sejong University, ... Yang, An infinite family of 3-designs from Preparata codes over Z 4 , Des. Codes Cryptogr. 15 (1998), no. 2, 175–181. [6] T. Helleseth, C. Rong, K. Yang, New infinite families of 3-designs...

Ngày tải lên: 07/08/2014, 15:22

... in infinite families of k-crossing-critical graphs? We positively answer one half of his question in Theorem 3.1 and Proposition 2.1; • namely we construct, for all k > 2, infinite families of ... 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 ver...

Ngày tải lên: 07/08/2014, 21:20

... given finite regular graph G =(V,E), let B = |B(v)| denote the size (indepen- dent of its centre) of a ball of radius one; let C be an identifying code. Since C is a covering of V ,thesphere-covering ... h3asacodeword: this allows the degree of g5toincreasebyoneonly(ifwetakei4andi6ascodewords). But then the covering of h2, f0andh0 requires an increase of the degree of g1ofa...

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

... 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 ... y i for 1 ≤ i ≤ k ) are finite. (See p. 135 of [1]). Another basic result is that all antichains of the partially ordered set of the finite words of a finite alp...

Ngày tải lên: 07/08/2014, 06:20

... 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 ... 10, and we extend it to infinite words by continuity. The infinite fixed point of µ beginning with 0 is denoted by t, hence t = 0110100110010110 ···. The infinite fixed poin...

Ngày tải lên: 07/08/2014, 06:22

... must consist of non-overlapping groups of terms of the product  n j=1   k =1 q j  . Hence we have m  i=1 n  j=1 σ j (x ij ) ≤ n  j=1  k  =1 q j  =1. The rest follows from the arithmetic-geometric ... contribute  tn sn  triples. Fix a value of t which contributes at least 1 n of the triples. Let 2 βn be the number of pairs of subsets of F with intersection of...

Ngày tải lên: 07/08/2014, 06:22

... 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

... accumulation points of infinite planar graphs, we generalize Tutte’s decomposition to include all infinite 2-connected graphs. 1 Introduction In [5], Tutte presents a decomposition of a finite 2-connected ... concerning accumulation points of infinite graphs embedded in the plane provides motivation for generalizing Tutte’s decomposition to infinite graphs. Question 1 Which (loca...

Ngày tải lên: 07/08/2014, 08:20

... of the authors of [CEF], to show this enumeration in helpmate form. Each of the next two problems shows an infinite sequence: the n-th term of the sequence is the number of ways White ... to many other kinds of mathematical chess problems. Thanks too to Tim Chow, one of the organizers of the conference, for soliciting the presentation and proofreading a draft of this articl...

Ngày tải lên: 07/08/2014, 08:22