Báo cáo toán học: "A combinatorial representation with Schr¨der paths of o biorthogonality of Laurent biorthogonal polynomials" pps

... for example. the electronic journal of combinatorics 14 (2007), #R37 9 A combinatorial representation with Schr¨oder paths of biorthogonality of Laurent biorthogonal polynomials Shuhei Kamioka ∗ Department ... certain kinds of Schr¨oder paths, which imply orthogonality and biorthogonality of LBPs. 1 Introduction and preliminaries Laurent biorthogonal polynomials...

Ngày tải lên: 07/08/2014, 15:22

... Kamioka, A combinatorial representation with Schr¨oder paths of biorthogonality of Laurent biorthogonal polynomials, Electron. J. Combin. 14 (2007), no. 1, Research Paper 37, 22 pp. (electronic). [8] ... weight of a piece the electronic journal of combinatorics 15 (2008), #R76 17 A combinatorial derivation with Schr¨oder paths of a determinant representation o...

Ngày tải lên: 07/08/2014, 21:20

... exactly one occurence of each one of N +1, ,N + m, and that the corresponding boxes form a ribbon r numbered from bottom to top and from left to right. Moreover, this ribbon can be cut out of P ... receivers associated with a given modulation method, which leads to the computation of various probabilities of errors (see again [18]). Among the different modulation protocols used in...

Ngày tải lên: 07/08/2014, 13:21

... electronic journal of combinatorics 6 (1999),#R40 12 [2] E. Barcucci, A. Del Lungo, E. Pergola, R. Pinzani, Some Combinatorial Interpretations of q–Analogs of Schr¨oder Numbers, Annals of Combina- torics, ... known as NSW numbers, and are related both to the order of simple groups [9] and to the solutions of the Diophantine equation: x 2 +(x+1) 2 =y 2 [8]. We will obtain a new b...

Ngày tải lên: 07/08/2014, 06:20

... k) box. For a more comprehesive introduction to the basics of partition theory, see [1]. 2 q-analogue of the Sum of Cubes In this section we introduce the following polynomial generalization of ... maintains some of the combinatorial properties of the classical formula, one might hope for a simpler formula. For this reason it may be of interest to investigate other q-analogues...

Ngày tải lên: 07/08/2014, 08:20

... ≤ ( n 2 ) of the numbers of permutations of length n having k inversions is log-concave. 1 Introduction Let p = p 1 p 2 ···p n be a permutation of length n, or, in what follows, an n-permutation. An ... inversion of p is a pair (i, j) of indices so that i<j, but p i >p j . The enumeration of n-permutations according to their number i(p) of inversions, and the study of...

Ngày tải lên: 07/08/2014, 08:22

... right-hand) side of (2). The aim of this paper is to find a combinatorial proof of (2). In Section 2 we construct the sets F bi n of labeled bicolored forests on [n]andD n of certain labeled bicolored binary trees, ... neighbor of n + 1 be a root. A graph is called bicolored if each vertex is colored with the color b (black) or w (white). We denote by F bi n the set of bicolo...

Ngày tải lên: 07/08/2014, 08:22

... v is a bijection from M to N. Moreover, an argument similar to that in the proof of Lemma 2.1 shows that inv(w)=inv(v). This completes the proof. 3 A Combinatorial Proof of Equation (1.8) Replacing ... of (1.5) in the framework of words, and in Section 3 the combinatorial proof of (1.8) using partitions of integers. Finally, in Section 4, we give a short proof of (1.3) from...

Ngày tải lên: 07/08/2014, 08:22

... real-orthogonal, the support of U(G) p , for some p, is presumably different from the support of M( −→ LD G ) p . This is because of the contribution of the negative entries in U(G). On the basis of ... statement of the proposition are mutually exclusive. Each case corresponds to U 3 (i,j),(l,m) > 0 for one of the cases A-F above. The condition 1 corresponds to the case A, 2 t...

Ngày tải lên: 07/08/2014, 13:21

... distributions are. We prove the above proposition in the next section and also expand it to give the proof of Theorem 1. 6 The stationary distribution for the M-PASEP and proof of Theorem 1 To prove ... distribution on this subset is simply related to that of the original chain. We also provide a direct proof of the validity of the weight equations. the electronic journal of combi...

Ngày tải lên: 07/08/2014, 13:21