Báo cáo toán học: " ON NONCROSSING AND NONNESTING PARTITIONS FOR CLASSICAL REFLECTION GROUPS " potx

... contains some concluding remarks and related questions. 2. Background and results Noncrossing partitions. We first recall the definition of noncrossing partitions for the classical reflection groups from ... address: athana@math.upenn.edu ON NONCROSSING AND NONNESTING PARTITIONS FOR CLASSICAL REFLECTION GROUPS CHRISTOS A. ATHANASIADIS Abstract. The number of n...

Ngày tải lên: 07/08/2014, 06:22

... theorems for con- densing and nonexpansive maps will be proved. 3.1. Condensing maps. Definition 3.3. Let Y be a nonempty and bounded subset of a Banach space X, and let γ denotes some measure of noncompactness ... Applications go to http://www.fixedpointtheoryandapplications.com/authors/instructions/ For information about other SpringerOpen publications go to http://www.springeropen...

Ngày tải lên: 20/06/2014, 20:20

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:21

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Ngày tải lên: 05/08/2014, 15:21

... 2 i−1 . [Note that s 0 (n)=r 0 (n)=0ifn=1,andis1ifn=1.] Proof. We use complete induction on n.Forn=5 or 7, we have k = 1. Since 5=3+2, and 7=3+4 are their only representations, s 1 (n)=r 1 (n)=1=2 0 ... +3  and (2.3) follows at once. Proofofclaim: We use induction on j.Forj= 1 the inequalities follow immediately from the fact that A 1 (0) = A 1 (1) = 1. Now assume the inequalities...

Ngày tải lên: 07/08/2014, 06:20

... present Noga Alon’s conjecture that n ∼ (k/2) 2 is the threshold for random permutations. Mathematics Subject Classification: 05A05,05A16. 1. Introduction Consider, for a permutation σ ∈S k ,thesetA(n, ... least one permutation in S k , i.e. G(n, k):=|∪ σ∈S k A(n, σ) |, where F (n, σ):=|A(n, σ) |. Simion and Schmidt [8], p. 398, give a formula for n! − G(n, 3), the number of n-permutat...

Ngày tải lên: 07/08/2014, 06:22

... 2002. [20] T. Motzkin, Relations between hypersurface cross ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for nonassociative products, Bull. ... cyclic permutation on the segment from position i to position j + 1. For the permutation 1, the reduced decomposition is the identity. Suppose that we have constructed the canonical...

Ngày tải lên: 07/08/2014, 07:21

... |S| = m and S contains no nonempty subsequence with zero sum, then f(S) ≥ 2m − 1. This answers an open question formulated by Gao and Leader. They proved the same result with the restriction (m, ... residual sequence contains one more distinct elements than T does, a contradiction to the choice of A 1 , . . . , A l . This shows that a ∈ A i for every i ∈ {1, . . . , l}. Therefore v g (S...

Ngày tải lên: 07/08/2014, 15:22

... ∞. References [1] Madras N and Slade G 1993 The Self-Avoiding Walk (Boston: Birkh¨auser) [2] Hughes B D 1995 Random Walks and Random Environments, Vol I Random Walks (Oxford: Clarendon) [3] Vanderzande C 1998 ... 2008 On q-functional equations and excursion moments Discrete Math., in press; math.CO/0503198 [34] Richard C 2006 Staircase polygons: moments of diagonal lengths and colum...

Ngày tải lên: 07/08/2014, 15:23