Báo cáo toán học: "New lower bounds for Heilbronn numbers" pps

... determination of optimal values and lower bounds for every H n . Besides the trivial cases H 3 and H 4 , Golberg showed constructions providing lower bounds for n ≤ 15. A.W.M. Dress, Yang Lu, ... lower bound for for Heilbronn s triangle problem in d dimensions. SIAM J. Discrete Math. 14 (2001), no. 2, 230–236. [3] C. Bertram–Kretzberg, T. Hofmeister, and H. Lefmann, An algori...

Ngày tải lên: 07/08/2014, 06:23

... Lower Bounds for Ramsey Numbers It is amazing that the result of this section has not been observed for the 25 years since [C] was published. Using this observation we will give 6 new lower bounds. Currently ... bound for R(5, 5, 5) was 169 given by Song [S], who more generally shows that R(5, 5, ,5    rtimes )≥4(6.48) r−1 +1 holds for all r.ForR(6, 6, 6) there was no esta...

Ngày tải lên: 07/08/2014, 06:20

... analogously. We refer the reader to [6] for a survey. 2 The Ramsey numbers for even cycles Up to now, there have been known only two exact values for 3-color Ramsey numbers for even cycles. More precisely, ... Moreover, by using upper bound for Ramsey number for even cycles ([5, Section 5.7, Theorem 10]), we have R 3 (C 8 ) ≤ 2412, and by using known upper bound for Ramsey numbe...

Ngày tải lên: 07/08/2014, 08:22

... 2413-occurrences. In this paper, we will improve this lower bound and introduce a generalized method involving weighted templates as a way for computing lower bounds for δ(π), the packing density of a non-layered ... proportion of subsequences of σ ∈ S n that are order-isomorphic to π. We generalize methods for obtaining lower bounds for the packing density of any pattern an...

Ngày tải lên: 07/08/2014, 15:23

... upper bounds on µ(n, d) appears in Deza and Frankl [10]: Theorem 1. For n  3 and d  n, µ(n, d)  n µ(n − 1, d) and therefore µ(n, d)  n! (d − 1)! In this paper, we will establish new bounds for ... Upper bounds for co nstant-weight codes. IEEE Transactions on Information Theory, 46(7):2373–2395, 2000. [2] V. B. Balakirsky and A. J. Han Vinck. On the performance of p ermutation...

Ngày tải lên: 08/08/2014, 12:22

... published bounds for S (5) are 157 ≤ S (5) ≤ 321, the lower bound was proved in [4] and the upper bound in [6]. For Ramsey numbers we know R 2 (3) = 6 and R 3 (3) = 17; the current bounds on R 4 (3) ... 1994; Accepted: September 18, 1994 Abstract For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K 3 . For integers m and n...

Ngày tải lên: 07/08/2014, 06:20

... Subject Classification: 05D10 Abstract We give two lower bound formulas for multicolored Ramsey numbers. These formu- las improve the bounds for several small multicolored Ramsey numbers. 1. INTRODUCTION In ... maximal Ramsey r-coloring. 2. THE LOWER BOUNDS We start with an easy bound which nonetheless improves upon some current best lower bounds. Theorem 2.1 Let r ≥ 3. For a...

Ngày tải lên: 07/08/2014, 06:23

... obtain the closed-form analytical solutions to CDF and PDF of the end-to-end SNR for TWOR-AF-Nodir systems, and present the corresponding tight lower bound. Though the tight lower bounds are obtained ... 2011:192 http://jwcn.eurasipjournals.com/content/2011/1/192 Page 5 of 8 RESEARCH Open Access Tight performance bounds for two-way opportunistic amplify-and-forward wireless relayi...

Ngày tải lên: 20/06/2014, 21:20

... value of γ(n, δ) for n ≤ 16, 0 ≤ δ ≤ n − 1 if the value is known, otherwise upper and lower bounds for γ(n, δ). We establish these values in Sections 2, 3 and 4. TIGHT UPPER BOUNDS FOR THE DOMINATION ...  4. γ(n, δ) for n ≤ 16. In Table 1 we give a list of values (or bounds) for γ(n, δ) when n ≤ 16. In this section we justify the entries of this table. See Table 3 in Appendi...

Ngày tải lên: 07/08/2014, 06:20

... 2.6939 18 2.6880 20 2.6832 22 2.6792 Table 2: Upper bounds for the connective constants µ (d,k) for walks with finite memory. The values shown are true upper bounds. 4 Acknowledgements We thank Tony Guttmann ... length 2 or 4 for any continuation of our walk, so it is not really neccessary to preserve the information that the previous step was taken at all – except for its contribu...

Ngày tải lên: 07/08/2014, 06:20