Báo cáo toán học: "A New Table of Constant Weight Codes of Length Greater than 28 " docx

... 94B60 Abstract Existing tables of constant weight codes are mainly confined to codes of length n ≤ 28. This paper presents tables of codes of lengths 29 ≤ n ≤ 63. The mo- tivation for creating these tables was ... of combinat orics 13 (2006), #A2 14 A New Table of Constant Weight Codes of Length Greater than 28 D. H. Smith, L. A. Hughes and S. Perki...

Ngày tải lên: 07/08/2014, 13:21

... proof for Claim 1. However, a short analysis of this proof yields a proof of Claim 2. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 C Fig. 1: Proof of ... the outline of the proof of Theorem 1. We think our proof of Theorem 1 could b e refined to give a better lower bound. However, we think t hat bound would be only slightly better tha...

Ngày tải lên: 08/08/2014, 01:20

... that there is no path of length 2 in G[S]. Next we establish that there is no path of length 1 in G[S]. Thus, S is an independent set in G. Hence a neighbor of a vertex of S in G is a large vertex ... bc(G; X) = 0 and sc(G; X) = 0. We show next that no vertex of X is a cut-vertex of G. Next we consider the set S of all vertices of G of degree 2 which do not belong to X;...

Ngày tải lên: 08/08/2014, 12:23

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:20

... define f(n) to be the size of the largest possible cancellative family of subsets of a n-set and f(k,n) to be the size of the largest possible cancellative family of k-subsets of a n-set. Note the ... difference. Let F 1 be a family of subsets of a n 1 -set, S 1 .LetF 2 be a family of subsets of a n 2 - set, S 2 . WedefinetheproductF 1 × F 2 to be the family of subsets of...

Ngày tải lên: 07/08/2014, 06:20

... proof of (3.2 ). Morse code sequences are finite sequences of dots (•) and dashes (−). We assume that a dot has length 1 and a dash has length 2. The number of all such sequences of total length ... illuminating combinatorial proof of (3.1 ), which is an adapta- tion of Franklin’s proof of the pentagonal number theorem to this case (cf. [1] or [4]). Let u beawordoflengthn −...

Ngày tải lên: 07/08/2014, 07:21

... dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. Let G be a connected graph of order ... journal of combinatorics 14 (2007), #R65 7 A new upper bound on the total domination number of a graph 1 Michael A. Henning ∗ and 2 Anders Yeo 1 School of Mathematical S...

Ngày tải lên: 07/08/2014, 15:23

... has been helpful in producing a combinatorial proof of integrality in some cases, many people pre- fer proofs of Laurentness versus other proofs of integrality. In [3], Fomin and Zelevinsky give ... journal of combinatorics 15 (2008), #R54 5 A New Family of Somos-like Recurrences Paul Heideman University of Wisconsin Madison, WI 53705 ppheideman@wisc.edu Emilie Hogan Department...

Ngày tải lên: 07/08/2014, 15:23

... classes of prime, reduced cycles of G. Ihara [6] defined zeta functions of graphs, and showed that the reciprocals of zeta functions of regular graphs are explicit polynomials. A zeta function of a ... unction of a hypergraph. A hypergraph H = (V (H), E(H)) is a pair of a set of hypervertices V (H) and a set of hyperedges E(H), which the union of all hyperedges is V (H)....

Ngày tải lên: 08/08/2014, 01:20