Báo cáo toán học: "Lower bounds for the football pool problem for 7 and 8 matches" pdf

... by 1, and the total sum is maximized under t his the electronic journal of combinatorics 16 (2009), #R89 3 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 Figure 4: The tra ... indicated in the left hand side of Fig. 13. Then f is not a source for any of the rectangles A 1 and A 2 . The right hand side of the same figure shows a solution...

Ngày tải lên: 08/08/2014, 01:20

... with n = 7 and s = 27 and get 8k 5 + 15k 6 + 22k 7 + 29  i 8 k i ≤ 58. (8) Multiplication with 3/22 and rounding off yields Lemma 3. the electronic journal of combinatorics 14 (20 07) , #R 27 4 5 Proof ... we show k 3 (7) ≥ 156 and k 3 (8) ≥ 402 improving on the best previously known bounds k 3 (7) ≥ 153 and k 3 (8) ≥ 3 98. The proofs are founded on a recent tech...

Ngày tải lên: 07/08/2014, 15:22

... throughout the paper and argue that these lemmas imply the validity of Theorem 1.1. The two main lemmas are proved in Sections 3 and 4 and these two sections correspond to the two parts of the proof ... for the base case, d = 1, let (v 0 , u 1 ) and (v 0 , u  1 ) be two different paths in T f,1 so that u 1 = u  1 . Let G 1 and G 2 be the labels of the nodes u 1...

Ngày tải lên: 07/08/2014, 21:21

... n. Theory Ser. B 57 (1993) 100–121. [6] J. Chen, J.L. Gross and R.G. Rieper, Lower Bounds for the Avera ge Genus, J. Graph Theory 19 (1995) 28 1–296. [7] J. Chen, A Linear-Time Algo r ithm for ... pairs of edges. Then, we apply Relation 1 and Operations 1,2 and 3 to normalize the polygon P and get the genus of the embedding. Based on joint trees, the topo lo gical...

Ngày tải lên: 08/08/2014, 12:23

... 343 K 7 (6, 3) 3 25 28 36 77 K 7 (7, 3) 4 99 101 1 27 343 K 7 (7, 4) 3 16 19 25 49 K 7 (8, 4) 4 56 58 76 343 K 7 (9, 4) 5 221 2 27 264 184 3 K 7 (8, 5) 3 11 17 20 49 K 7 (9, 5) 4 35 39 52 323 K 7 (10, ... 382 512 K 8 (6, 3) 3 35 40 52 1 07 K 8 (7, 3) 4 161 171 196 512 K 8 (7, 4) 3 22 24 37 92 K 8 (8, 4) 4 89 96 1 18 512 K 8 (8, 5) 3 15 22 29 90 ‡ K 8 (9...

Ngày tải lên: 08/08/2014, 01:20

... grid, then D(C)  6 2b 2 + 4 + 6 = 6 30 = 1 5 .  4 Lower Bounds for the Square Grid Lemma 8 establishes an upper bound of 8 for the degree of the graph Γ formed by an r-identifying code in the ... Bound for the Hexagonal Grid Lemma 7 establishes an upper bound of 6 for the degree of the graph Γ formed by an r-identifying code in the hex grid, which allows us t...

Ngày tải lên: 08/08/2014, 12:22

... v T Dv ≥ 0 for every v ∈ T Δ (x) ∩ (∇f(x)) ⊥ , where (∇f(x)) ⊥ = {v ∈ R n : ∇f(x)v =0}. The ideas of the proof of Theorem 2.2 are adapted from [8, Theorem 4.1] and [12, Theorem 6]. In [8] , some ... programming, Math. Progr am. 1 (1 971 ) 359–365. 7. H. X. Phu and N. D. Yen, On the stability of solutions to quadratic programming problems, Math. Pr ogram. 89 (2001) 385 –394. 8....

Ngày tải lên: 06/08/2014, 05:20

... 01021324354 68 573 45 670 81 2345130243546 576 87 8 , x 10 = 010213243546 579 683 45 6 78 09123456130243546 576 87 9 89 . We note that the words x k are symmetric in the sense that reversing x k produces the same result ... 0w 1 ···w 7 . The length of 0w 1 ···w 7 is at least (4) (8) − 5 = 27. The length of w 4 w 5 w 6 w 7 is either 8 or 10, where in the latter case, th...

Ngày tải lên: 07/08/2014, 08:20

... Kolmogorov theory for the next section and thus give a short intro- duction here. For a fuller and more rigorous account of Kolmogorov Theory see the book by Li and Vitanyi [15]. What makes a string random? ... Proceedings of the London Mathematical Society, 2:4 17 439, 1952. [7] P. Erd¨os and J. Selfridge. On a combinatorial game. Journal of C ombinatorial Theory, Series A...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 05/08/2014, 15:21