Báo cáo toán học: "A short proof for the number of permutations containing pattern 321 exactly once" ppt

... 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 precise, Noonan considered permutations ... A short proof for the number of permutations containing pattern 321 exactly once Alexander Burstein Department of Mathematics Howard...

Ngày tải lên: 08/08/2014, 14:23

... 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...

Ngày tải lên: 07/08/2014, 08:22

... (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, the error term in the second ... to thank the referee for numerous comments and suggestions which have led to a substantially improved paper. An Asymptotic Expansion for the Number of Permutatio...

Ngày tải lên: 07/08/2014, 06:20

... +32t − 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 ... 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 same length which leads to...

Ngày tải lên: 07/08/2014, 06:22

... : 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

... 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. ... ). Finally, recall that the conjugate of a partition λ is the partition λ  obtained by flipping the diagram of λ across the NW-SE axis; it follows that λ  i co...

Ngày tải lên: 07/08/2014, 15:22

... A short proof The following theorem first appeared in [3, Theorem 31, pp. 447–457]. (Actually, this is not quite true. The theorem there was claimed only for uncountable orders into which neither ... combinatorics of orders, and most especially in their Ram- sey theory, first described and investigated by P. Erd˝os and R. Rado in [3]. In its most straightforward form, Ramsey theory...

Ngày tải lên: 07/08/2014, 06:20

... ···(x−n+1). Then we have the following reciprocity theorem. Theorem. For any board B ⊂ [d] × [d], R(B; x)=(−1) d R(B; − x − 1). The existing proofs derive this as a corollary of other reciprocity theorems, ... secondary subject numbers: 05A05, 05A15 A board B is a subset of [d] × [d](where[d]isdefinedtobe{1, 2, ,d})andtherook numbers r B k of a board are the number of subsets...

Ngày tải lên: 07/08/2014, 06:20

... containing e and a 1-factor avoiding e, then G has a k-factor containing e and a k-factor avoiding e for every k ∈ {1, 2, . . . , r − 1}. Proof. Let F and F e be two 1-factors of G containing ... even order. If for every edge e of G, G has a 1-factor containing e, then G has a k-factor containing e and another k-factor avoiding e for all integers k with 1 ≤ k ≤ r − 1. Th...

Ngày tải lên: 07/08/2014, 13:21

... 2.4: The “if” part in Theorem(2.3), which is a particular case of the Alexandrov- Fenchel inequalities, is not simple, but was proved seventy years ago [1]. The proof of the “only if” part in Theorem(2.3) ... that the convolution of logconcave sequences is also logconcave was proved in [3] in 1949. We present in this paper a short proof of Theorem(1.1). 2 The Minkows...

Ngày tải lên: 07/08/2014, 21:21