Báo cáo toán học: "Climbing elements in finite Coxeter groups" ppt

... combinatorics 17 (2010), #R156 4 Climbing elements in finite Coxeter groups Thomas Brady School of Mathematical Sciences Dublin City University, Glasnevin, Dublin 9, Ireland tom.brady@dcu.ie Aisling ... domain C to w(C) which crosses hyperplanes in increasing order. In this paper, we characterise the climbing elements in the case where the reduced expression for w 0 is obtain...

Ngày tải lên: 08/08/2014, 12:23

... theory. Integral graphs in these classes were given by using number theory and computer search. In this paper, a new method of constructing fifteen in nite classes of integral graphs is presented. In ... Cao, Integral trees of diameter R (3 ≤ R ≤ 6) (in Chinese), Heilongjiang Daxue Ziran Kexue Xuebao (2) (1988) 1-3, 95. [4] Z.F. Cao, Introductory Diophantine Equations (in Chinese), Ha...

Ngày tải lên: 07/08/2014, 15:22

... of the parts of λ, or by inserting a part of size 1 into λ. We employ the methods they developed in order to study the same problem for the following poset, which is of interest because of its ... underlying set is the same, but µ covers λ if µ can be obtained from λ by adding 1 to one of the parts of λ, or by inserting a part of size 1 at the left or at the right of λ. We calculate generat...

Ngày tải lên: 07/08/2014, 08:22

... vertices in graphs, IEEE Transactions on Information Theory, vol 44, pp. 599-611, 1998. [6] A. Lobstein, Bibliography on identifying and locating-dominating codes in graphs, http://www.infres.enst.fr/∼lobstein/debutBIBidetlocdom.pdf [7] ... minimal r-twin-free graph for the induced subgraph relationship. Indeed, we have: the electronic journal of combinatorics 15 (2008), #N17 5 An r-twin-...

Ngày tải lên: 07/08/2014, 15:22

... evident that any zero-sum free sequence S in G can be extended into an unex- tendible sequence. We can extend S by choosing a series elements g 1 , . . . , g r in a nat- ural process such that |  (Sg 1 )| ... D. Gao and A. Geroldinger, On Long minimal zero sequences in finite abelian groups, Periodica Math. Hungarica, 38(3)(1999), 179-211. [3] W. D. Gao, An addition theorem for...

Ngày tải lên: 07/08/2014, 15:22

... checking if the given graph is (d; ε 1 , ε 2 )-regular we need to consider only sets of the size ε 1 |V i |, i = 1, 2. In the following section we state our main results proved in Sections 3. In ... bipartite subgraph that can be contained in a (d; ε)-regular graph. 3 The Proof of Theorem 2.1 Before we prove Theorem 2.1, we state a result showing how, by using random graphs, one can fi...

Ngày tải lên: 07/08/2014, 15:23

... eparating family on Ω = [n] with elements labelled i n order of increasing degree. The n if 1 ≤ i < j ≤ n there exists A ∈ S with j ∈ A, i /∈ A. Proof. Since S is separating, there is some A in ... A j since j ∈ A i , j /∈ A j . The main result of this section follows easily. Theorem 3. Let S be a separating union-closed family on Ω(S) = [n] with elements labelled in order of incre...

Ngày tải lên: 08/08/2014, 14:23

... k elements in their labeling sequence, each block forms a ma ximal clique of Inf k (K n ). The graph formed by contracting each of these maximal cliques to a single vertex is Inf k−1 (K n ). Since ... obtained from G by attaching the graph A |G| shown in Figure 3 to G by identifying the vertex a in A |G| with the vertex v 1 in G. Otherwise, let G ′ be the graph obtained from G by at...

Ngày tải lên: 07/08/2014, 21:21

... [2]). In [1], Biggs introduced perfect codes in graphs. From this point of view, a perfect binary single-error correcting code of length k is a perfect code on the hypercube Q k ,and a tiling of ... in nite length. Both existence and nonexistence results are given. 1 Introduction Perfect codes appeared in error correcting codes theory during the late 40’s with the work of Golay and Ham...

Ngày tải lên: 07/08/2014, 13:21

... lie in A ∪ {0}. Set E = E 1 × E 2 . Since E 1 has its dot product set contained in A, and E 2 has its dot product set contained in A ∪ {0}, we know that any dot product of two elements in E is in ... taking the union of about q 2 lines through the origin, such that no two lines are perpendicular, and removing the union of their q 2 orthogonal complements, which are lines perpendic...

Ngày tải lên: 07/08/2014, 21:21