Báo cáo toán học: "Perfect codes in Cartesian products of 2-paths and infinite paths" pptx

... 05C69,05C70,94B60 Abstract We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and ... +1+2n is a factor of 2 k ,andthereissomep such that 2n + k =2 p − 1. the electronic journal of combinatorics 12 (2005), #R65 7 Perfect codes...

Ngày tải lên: 07/08/2014, 13:21

... is interesting in itself and has been usefully applied to other families of graphs [8]. We describe the method in Section 3, after a short introduction to the Tutte polyonmial in Section 2. In ... Chang and R. Shrock, Acyclic orientation numbers for families of graphs, State Univ. of New York at Stony Brook preprint. [5] N.J. Calkin and H.S. Wilf, The number of independe...

Ngày tải lên: 07/08/2014, 07:21

... connection coincide. Among other things, we will be interested in compactifications of G, which, for in nite graphs, means adding some additional points and open sets corresponding to the “ends” of G. An ... Z X of X is contained in the cycle space Z Y of Y . In this work, we show how to extend a basis for Z X to a basis of Z Y . 1 Introduction Bonnington and Richter [1] i...

Ngày tải lên: 08/08/2014, 14:23

... contradiction since φ  is a distinguishing k-labeling of T  . Thus, φ is a distinguishing k-labeling of T so D(T ) ≤ D(T  ). By the same argument, we can show that every distinguishing k-labeling of T  can ... trees. 3 Distinguishing labelings of rooted trees In this section, we give a characterization of the distinguishing labelings of rooted tree T ,and show how we can de...

Ngày tải lên: 07/08/2014, 13:21

... 2k + 1, and, since the cardinality of T is at most l(|A|− 1) + 1, f(¯α, p) + 1 = |A| ≥ log p l log 2k + 1, completing the proof of Theorem 1. Since l ≤ k as an immediate consequence of Theorem ... A. Schinzel, Addition of sequences in general fields, Monatshefte f¨ur Mathematik 82 (1976), 261–268. [2] D. L. Hilliker, E. G. Straus, Uniqueness of linear combinations (mod p), Journal...

Ngày tải lên: 07/08/2014, 15:22

... electronic journal of combinatorics 17 (2010), #N24 2 Elementary Proofs for Convolution Identities of Abel and Hagen–Rothe Wenchang Chu ∗ Hangzhou Normal University Institute of Combin atorial Mathematics Hangzhou ... Chu, Invers i on Tec hniques and Combinatorial Identities: A quick introduction to hypergeome tric ev aluations, Math. Appl. 283 (1994), 31 –57. [2] W. Chu, Generating...

Ngày tải lên: 08/08/2014, 11:20

... structure of a minimum dominating set of C n 2n+1 , the Cartesian product of n copies of the cycle of size 2n + 1, where 2n + 1 is a prime. Keywords: Perfect Lee codes; dominating sets; defining sets. 1 ... one perfect dominating set, a set S ⊆ V (G) is a minimum dominating set if and only if it is a perfect dominating set. In [2] Chartrand et al. studied the size of definin...

Ngày tải lên: 07/08/2014, 13:21

... Perfect matchings in -regular graphs Noga Alon ∗ School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540 and Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact ... side, and is an easy consequence of the Minc conjecture [6] for permanents, proved by Br´egman [2] (c.f. also [1] for a probabilistic description of a proof of Schrijver)....

Ngày tải lên: 07/08/2014, 06:22

... a subset S R of R and an integer α with 0 ≤ α<w;thesetS obtained as the union of the classes of the elements of S R in the tiling induced by the translations of vectors (w,0) and (α, h)isa periodic ... identifying radius of codes. In: Proceedings of the 7th Nordic Combinatorial Conference (eds. T. Harju and I. Honkala), Turku, 1999. [14] I. Honkala, A. Lobstein: On...

Ngày tải lên: 07/08/2014, 06:23

... 2-fa ctor of H using many of the specified edges of H so that when transforming this 2-factor of H to that of G, each of those edges of H has many ways to make 2-factors of G. 2 Structure of 2-edge-connected ... strings of diamonds and replacing each vertex of H with a triangle. Since D is chosen maximally, u and v are not in diamonds and therefore H has the edge...

Ngày tải lên: 08/08/2014, 14:22