Báo cáo toán học: " A Combinatorial Derivation of the PASEP Stationary Stat" pps

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Ngày tải lên: 05/08/2014, 09:46

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Ngày tải lên: 05/08/2014, 15:20

... second coordinate (i.e., the number of ways of “placing k non-taking rooks on B”). It has long been known [5] that the rook numbers of a board B determine the rook numbers of the complementary board ... subset of [d] ì [d](where[d]isdenedtobe{1, 2, ,d})andtherook numbers r B k of a board are the number of subsets of B of size k such that no two elements have t...

Ngày tải lên: 07/08/2014, 06:20

... bijective proof for this recurrence in terms of the area of Schrăoder paths. In 1976 Kreweras [7] proved that the sum of the areas of the regions lying under the elevated Schrăoder paths satisfies ... satisfies the recurrence relation and then establishing a bijection between the set of these paths and the set of triangles constituting the total area of...

Ngày tải lên: 07/08/2014, 06:20

... extension of the Littlewood-Richardson rule [Z]. Taking the specialization λ = , we obtain the decomposition of s à/ into Schur functions; it is simpler than the traditional formulation of the Littlewood-Richardson rule ... the same tableaux. Via the specialization ν = , we obtain yet another formulation of the Littlewood- Richardson rule in this case involving th...

Ngày tải lên: 07/08/2014, 06:23

... number of boxes in the first row is equal to the size of the first part, the number of boxes in the second row is equal to the size of the second part, etc. For example, the Ferrers diagram for the ... 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 generalizat...

Ngày tải lên: 07/08/2014, 08:20

... Subject Classifications: 0 5A0 5, 0 5A1 5 To Richard Stanley, who introduced me to the area of log-concave sequences. Abstract We provide a combinatorial proof for the fact that for any fixed n, the sequence {i(n, ... A Combinatorial Proof of the Log-concavity of a famous sequence counting permutations Mikl´os B´ona ∗ Submitted: Nov 24, 2004; Accepted: Jan...

Ngày tải lên: 07/08/2014, 08:22

... electronic journal of combinatorics 11(2) (2005), #N3 3 A combinatorial pro of of Postnikov’s identity and a generalized enumeration of labeled trees Seunghyun Seo ∗ Department of Mathematics Brandeis ... left-hand (resp. 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...

Ngày tải lên: 07/08/2014, 08:22

... generalization of the famous q-Pfa-Saalschăutz identity. An elementary proofofthisidentityisalsogiven. 1 Introduction Throughout this paper we regard q as an indeterminate, and we follow the notation ... electronic journal of combinatorics 12 (2005), #N2 4 A Combinatorial Proof of a Symmetric q-Pfa-Saalschăutz Identity Victor J. W. Guo Center for Combinatorics, LPMC Nankai...

Ngày tải lên: 07/08/2014, 08:22

... define a larger Markov chain, the M -PASEP, which we use to study the stationary distribution of the original PASEP. In particular we show that the stationary distributions of the M -PASEP and the PASEP ... 2006 Mathematics Subject Classifications: 0 5A9 9, 60G10 Abstract We give a combinatorial derivation and interpretation of the weights associated with th...

Ngày tải lên: 07/08/2014, 13:21

... of parts of λ is called the length of λ, denoted by l(λ). The weight of λ is the sum of parts, denoted by |λ|. We let P(n) denote the set of partitions of n. Let spt(n) denote the number of smallest ... give a combinatorial proof of Andrews’ smallest parts partition function with the aid of rooted partitions introduced by Chen and the author. 1 Introductio...

Ngày tải lên: 07/08/2014, 15:22

... weight of a piece the electronic journal of combinatorics 15 (2008), #R76 17 A combinatorial derivation with Schrăoder paths of a determinant representation of Laurent biorthogonal polynomials Shuhei ... interpretation [2] of Jacobi type continued fractions (J-fractions), a combinatorial interpretation in terms of Motzkin and Favard paths. Specifically h...

Ngày tải lên: 07/08/2014, 21:20

... l property of trees which was observed by Bruns and Hibi [2]. the electronic journal of combinatorics 17 (2010), #R9 6 A combinatorial proof of a formula for Betti numbers of a stacked polytope Suyoung ... Choi ∗ Department of Mathematical Sciences KAIST, Republic of Korea choisy@kaist.ac.kr (Current) Department of Mathematics Osaka City University, Japan ch...

Ngày tải lên: 08/08/2014, 11:20

... t). The basic idea of the proof of Theorem 3.1 is to show F à (q, t) and G à (q, t) satisfy the same recursion in the hook case. Proof. We first note the Garsia-Haiman recursion for the Hilbert series ... to the product of the weights of each of its entries, here the weight of entry s in T is taken to be the weight of the corner square containing s in...

Ngày tải lên: 08/08/2014, 12:22

... respectively down to ⌈ ⌉ ⌊ ⌋ the electronic journal of combinatorics 17 (2010), #R176 5 A Paintability Version of the Combinatorial Nullstellensatz, and List Colorings of k-partite k-uniform Hypergraphs Uwe ... ame-theoretic setting in Section 4. The definitions and proofing ideas in this section generalize the introduction of paintability of graphs in [...

Ngày tải lên: 08/08/2014, 12:23