Báo cáo toán học: "A sharp bound for the reconstruction of partitions" ppt

... agree above row r and to the left of column c (and the definitions of r and c) we see that the only possibility for λ/µ is (r, c), completing the proof of this case and the theorem. Acknowledgements. ... 308, 9 (2008), 1524–1530. the electronic journal of combinatorics 15 (2008), #N23 4 A sharp bound for the reconstruction of partitions Vincent Vatter Departme...

Ngày tải lên: 07/08/2014, 15:22

... 1. Then f(n) ≥ n +32t − 1, for n ≥ n t . This completes the proof of the theorem. From the above theorem, we have lim inf n→∞ f(n) − n √ n ≥  2+ 2562 6911 , which is better than the previous bounds √ 2(see[2]),  2+ 487 1381 (see ... denote the number of vertices, and (G) denote the number of edges. In this paper, we construct a graph G having no two cycles with the sa...

Ngày tải lên: 07/08/2014, 06:22

... s 2 n . (1) where b(i) is the number of times the integer i occurs in the sequence T . Note that the sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T . 3 A simple proof for the existence of exponentially balanced ... code the transition counts of which are all the same power of two, or are two successive powers of two. A proof for the existence of e...

Ngày tải lên: 07/08/2014, 08:22

... : the uppermost cell of the rightmost column of the polyomino has the maximal ordinate among all the cells of the polyomino; U2 : the lowest cell of the rightmost column of the polyomino has the ... interpretation of the closed formula (10) for the number of con- vex permutominoes. We remark that the expression of f n resembles the expression (1)...

Ngày tải lên: 07/08/2014, 15:22

... exactly once. In this paper, we give a short proof for the result of Noonan [3] that the number of permutations of length n containing exactly one occurence of pattern 321 is 3 n  2n n−3  . (To be ... A short proof for the number of permutations containing pattern 321 exactly once Alexander Burstein Department of Mathematics Howard University Washington, DC ... π 1 cπ...

Ngày tải lên: 08/08/2014, 14:23

... 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 ,let[ m, n ]denotetheset{ i | m ≤ i ≤ n }.AsetSof integers ... defined to be the smallest integer t , such that in any k-coloring of the edges of K t , there is a complete subgraph K n all of whose edges have the same color. A su...

Ngày tải lên: 07/08/2014, 06:20

... 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 condition A ∪ B = A ∪ C ⇒ B = C isthesameastheconditionBC ... denotes the symmetric 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...

Ngày tải lên: 07/08/2014, 06:20

... set of MOFS of type F (km; k). Proof. This is the case λ = 1 of the theorem. Remark 3 Laywine proves the above corollary (see [1, IV.20.8(3)],[2] or [3]) for the case when k is a power of m. Corollary ... m. Corollary 4 If there exists an affine plane of order m and complete set of type F (λm 2 ; λ), then there exists a complete set of type F (λm 2 ; λm). Proof. This is...

Ngày tải lên: 07/08/2014, 06:20

... the asymptotic expansion of B(n)/n!withO(n −9/2 ln 19 n). The following extension of Theorem 1 (the case m = 3) giving a complete asymptotic expansion of I(n, x) can be immediately read out of ... (17) where the last equation follows from (7). The error term in the first equation holds uniformly for all real numbers x by the comments after (15) and, since | cos(ux)|≤1,...

Ngày tải lên: 07/08/2014, 06:20

... presentation of the fundamental group of the knot complement. For a square matrix M with entries in CG the trace tr CG (M) denotes the coefficient of the unit element in the sum of the diagonal elements. The ... k −2 AA ∗ ) n  (4) The value of k can be chosen to be the product of (g −1) 2 and the maximum of the 1-norm of the entries in A (see [L¨uc94...

Ngày tải lên: 07/08/2014, 15:23