Báo cáo toán hoc:" Profiles of permutations " pdf

... number of cycles of a permutation of [n] with all cycle lengths even. The following two results give a decomposition of the number of cycles of permutations with all cycle lengths even into a sum of ... that for large n, 10% of elements of 1/2-weighted permutations are in cycles of length at least 0.99 n. If we define the “co-length” of a cycle of a permutation to b...

Ngày tải lên: 08/08/2014, 01:20

... Enumerations for Permutations in the Set V P n (S) In this section, we will consider enumerative problems of permutations in the set V P n (S). Let vp n (S) denote the number of permutations in ... is called an n-left factor of Dyck paths. Let L n denote the set of all n-left factors of Dyck paths. For any i  0, let L n,i denote the set of all n-left factors of Dyck paths...

Ngày tải lên: 08/08/2014, 12:22

... S n (p 1 , . . . , p k ) the set of permutations of length n avoiding all of the p i and by A n (p 1 , . . . , p k ) the set of alternating permutations of length n avoiding all of the p i , and we set ... Wilf classes of pairs of permutations of length 4. Electronic J. Combinatorics, 12:R25, 2005. [5] T. Mansour. Restricted 132-alternating permutations and Chebyshev...

Ngày tải lên: 07/08/2014, 21:21

... S n (τ)todenotethesetofτ-avoiding permutations in S n and, more generally, S n (T ) for the set of all permutations of length n which avoid each pattern of the set T . A central theme in the theory of pattern-avoiding ... number of elements of S n (B m ) (or, equivalently, S n (A m )) was determined in [2]. Recently, research into the enumeration of permutations having a p...

Ngày tải lên: 07/08/2014, 07:21

... antichain. If X is any set of permutations, we let A(X) denote the set of finite permutations that avoid every member of X. We also let cl(X)denotetheclosure of X,thatis,thesetof all permutations p such ... j of P n for some i ∈ [2,m− 1], then batch i +1ofP m is mapped into a batch of P n of numbered at most j +1,and (ii) batch 1 of P m must be mapped into batch 1 of P n...

Ngày tải lên: 07/08/2014, 07:21

... tree of permutations. (b) Nodes labeled by the length of the permutations. 1 Introduction 1.1 Pattern-avoiding permutations and generating trees Let σ = σ 1 σ 2 ···σ n be a permutation of length ... instance, all permutations of length 4 are Baxter permutations except 2413 and 3142 (check i =2). Our aim is to recover and refine the following result. Theorem 1 The number of B...

Ngày tải lên: 07/08/2014, 07:21

... understanding of the structure of all permutations in S n (1342, 3124). We shall see that the structure of permutations in S n (1243, 2134) is very similar. 2.4 The Structure of Permutations in ... takes permutations that do not begin with n to permutations that do not begin with 1. We now move on to the next theorem. Proof of Theorem 2: Let S nk (1342, 3124) denote the se...

Ngày tải lên: 07/08/2014, 08:22

... of the FWHM of L1 emission lines for a series of Mn concentrations. Figure 4. The emission intensity of the neutral acceptor-bound exciton line L1. The emission intensity is a function of ... around the vacancy site, thus softening the normal-mode frequencies of the lattice and reducing the zero-point energy of the oscillators. An increase in the number of Mn atoms in t...

Ngày tải lên: 20/06/2014, 20:20

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Ngày tải lên: 20/06/2014, 20:20

... The calculation of the contents of the Al 2 O 3 in the composite thick films: (a) the Hashin-Shtrikman bounds of contents of Al 2 O 3 in composite thick films as a function of measured relative ... dielectric properties of the films. Figure 1 shows the XRD patterns of deposited films with different mixing ratios of the Al 2 O 3 starting powder. The α-Al 2 O 3 phase o...

Ngày tải lên: 20/06/2014, 20:20