Báo cáo toán hoc:"On Suborbital Graphs for the Normalizer of Γ0(N )" pot

... Journal of Combinatorics 27 (2006) 193- 206.], that when the normalizer of Γ 0 (N) acts transitively on Q ∪ {∞}, any circuit in the suborbital graph G(∞, u/n) for the normalizer of Γ 0 (N), is of the ... Theorem3.1, C ∗ is of the form v → T (v) → T 2 (v) → T 3 (v) → · ·· → T k−1 (v) → v the electronic journal of combinatorics 16 (2009), #R116 13 On Suborbital...

Ngày tải lên: 08/08/2014, 01:20

... Yet another reformu- lation shows that the cycle index series is also  T ∈T Z(Aut(T )), where Z(Aut(T )) is the cycle index of the automorphism group of T . The following formula for the cycle ... Proof of the main theorem By the recursive structure of rooted trees and the multiplicative properties of the cycle index, it is not difficult to see that Z = Z T (s 1 ,...

Ngày tải lên: 07/08/2014, 13:21

... 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

... +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 ... 799). Now we define these B i ’s. These subgraphs all have a common vertex x, otherwise their vertex sets are pairwise disjoint. For 7t+1 8 ≤ i ≤ t − 742, let the subgraph B 19t...

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

... 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. ... k-deletion of µ can contain the cell (k, k + 1) and that no k-deletion of λ can contain the cell (k + 1, k). Therefore every k-deletion of µ and of λ is actually...

Ngày tải lên: 07/08/2014, 15:22

... : 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

... Stirling’s formula yields the desired result. The proposition is proved. 3 Proofs of Theorems and Corollaries The claim of Theorem 1 follows from Proposition 2. We will discuss only the remaining statements. Proof ... virtue of 1 − cos τ ≍ τ 2 for |τ|  π , the last integral is of order k −3/2 . This and Stirling’s formula yield the desired asymptotic formula in the se...

Ngày tải lên: 08/08/2014, 12:22

... bound obtained by application of Theorem is 9 µ(6, 5, 5)  34. For this reason, the upper bounds do not contribute to any improvement of the results given by Theorem 7 for the range of values considered ... columns, their symbols and up to the inversion. It immediately follows from this theorem that the autormorphism group of the conjugacy scheme of S n is precisely...

Ngày tải lên: 08/08/2014, 12:22

... 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