Báo cáo toán học: "On Kissing Numbers in Dimensions 32 to 128" pptx

... 07 932- 0971, USA Submitted: April 9, 1998; Accepted: April 13, 1998 ABSTRACT An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128. 1. Introduction Let ... 1,260,230,400 in dimensions 32, 64 and 128, for example). In contrast, Quebbemann’s lattice Q 32 [14], [5, Chap. 8] has τ = 261,120. In recent years the kissing...

Ngày tải lên: 07/08/2014, 06:22

Ngày tải lên: 05/08/2014, 15:20

... 143–148. 3. J. W. Moon, Topics on Tournaments Halt, Rinehart and Winston, New York, 1968. 4. K. B. Reid and L. W. Beineke, Tournaments, Selected Topics in Graph Theory, L.W. Beineke and R.J. Wilson, ... appeared in Chinese [6] in 1988 and in English [7] in 1989. In the following result, we prove that any set of p non-negative integers s 1 ,s 2 , ,s p with s 1 <s 2 < < s p...

Ngày tải lên: 06/08/2014, 05:20

... disjoint subsets D, S of V (G), whether G has a k-factor or not. In 1985, Enomoto, Jackson, Katerinis and Saito [3] proved the following result. Lemma 2.2 Let G be a graph and k a positive integer ... eccentricity of vertices into ∗ corresponding author the electronic journal of combinatorics 11 (2004), #R7 1 For regular graphs without a k-factor, for odd k, we can give the following result...

Ngày tải lên: 07/08/2014, 08:20

... a useful consequence. In Section 3, we outline Shen’s proof of his bound on α in [5]. In Sections 4 and 5 we prove Theorem 2. In Section 6 we outline a part of the proof in [4] and prove Theorem ... so that the resulting digraph D  is acyclic. If true, this conjecture would imply the following strengthening of Lemma 5: Each digraph D obtained from a tournament by deleting k edges,...

Ngày tải lên: 07/08/2014, 13:21

... two non-codewords in F(i, j) are in the lower-left and upper-right corners (in the other case, we just go up instead of going down in what follows: as explained above, the voting rule is symmetric in this ... identifying codes in graphs, Information Processing Lett., 102 (2007), pp. 92–98. the electronic journal of combinatorics 15 (2008), #R3 12 2 Unknown edge deletions We begin b...

Ngày tải lên: 07/08/2014, 15:22

... It is natural to ask for a combinatorial interpretation. Lattice path techniques have been shown to be useful in solving the unimodality problem. As an example, we present a combinatorial proof ... Q 1 , Q 2 into three subpaths q 1 , q 2 , q 3 . Let p  1 be obtained by moving p 1 down to Q 1 south δ−d units and p  3 be obtained by moving p 3 right to Q 2 east δ units. Then we obta...

Ngày tải lên: 07/08/2014, 21:20

... hope is to determine not only the winner of a game, but also how fast is he able to win. For a game F, let τ E (F) be the smallest integer t such that Enforcer ha s a strategy to win the game F in ... later Hefetz et al. [7] studied the fast winning in Maker-Breaker Hamiltonicity game. We would like to emphasize that, generally speaking, results on fast winning in po- sitional g...

Ngày tải lên: 08/08/2014, 12:22

... O(L −1 ). Inserting this expression into the previous equality and integrating we obtain the desired result (10). To prove (11 ) , we first restrict the region to 1  k  √ m where all obtained remainder term ... R. Finally, we observe that these results can be used to obtain asymptotical formulas for max mk d k (m) as k → ∞. We intend to discuss that in a forthcoming paper. 2 The s...

Ngày tải lên: 08/08/2014, 12:22

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