Báo cáo toán học: " Two Simple Proofs of Winquist’s Identity" doc

... (−1) m q (3m 2 +m)/2 c 2 , the electronic journal of combinatorics 17 (2010), #R116 2 Two Simple Proofs of Winquist’s Identity Chutchai Nupet Department of Mathematics Faculty of Science, Pr ince of Songkla University Hatyai, ... Classifi cation: 11F20, 11F27 Abstract We give two new proofs of Winquist’s identity. In the first pro of, we u se basic properties of cub...

Ngày tải lên: 08/08/2014, 12:22

... transpose two of the rows or two of the columns in the corresponding diagram. One must be careful, however, to preserve row and column sums. If two of the row sums are the same, or if two of the ... bijective proof of Borchardt’s identity, one which relies only on rearranging terms in a sum by means of sign-reversing involutions. The proof reveals interesting properties o...

Ngày tải lên: 07/08/2014, 08:20

... complete proof of theorem. By the same technique, we derive the following equivalent form of Eq. (1.3). the electronic journal of combinatorics 13 (2006), #R52 5 Two finite forms of Watson’s quintuple ... pair of functions f(x, y)=1− xy, g(x, y)=x − y. Consequently, we get the special case of Theorem 3 with these parameters x i = aq i ,b i = q i , which is restated in terms of...

Ngày tải lên: 07/08/2014, 13:21

... (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 labeled bicolored forests on [n]andD n of certain labeled ... generalizations of |T n+1 | =(n +1) n and |P n+1 | =(n +1)!C n . Remark. In spite of the simple expressions, we have not proved (8), (11) and (12) in a bijective way. Also a dire...

Ngày tải lên: 07/08/2014, 08:22

... 2000 Abstract: We prove two extensions of the Hales-Jewett coloring theorem. The first is a polynomial version of a finitary case of Furstenberg and Katznelson’s multiparameter elaboration of a theorem, ... contained in equation (2.3) of [FK]. For another proof, see [M1, Lemma 2.3.3]. Lemma 2.10 Let X be a compact space and let k ∈ N.IfA, B ⊂ (X X ) k and A consists of k-tuples o...

Ngày tải lên: 07/08/2014, 06:20

... Π n and the set of domino tilings of AD n based on an idea, due to D. Randall, mentioned in [8, Solution of Exercise 6.49]. the electronic journal of combinatorics 12 (2005), #R18 4 A Simple Proof of the ... Kirkland [2] give a proof by considering a matrix of order n(n +1) the determinant of which gives a n . Their proof is reduced to the computation of the determinant of...

Ngày tải lên: 07/08/2014, 08:22

... extensions to two classical determinantal results of Bressoud and Wei, and of Koike. The proofs in that paper were algebraic. The present paper contains combinatorial lattice path proofs. Keywords: ... [5] provides proofs of certain generalizations of two classical determinan- tal identities, one by Bressoud and Wei [1] and one by Koike [8]. Both of these identities are ex...

Ngày tải lên: 08/08/2014, 12:23

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Ngày tải lên: 05/08/2014, 10:20

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Ngày tải lên: 05/08/2014, 15:20

... completed the proof of equation (1.4). 5 Proof of Equation 1.5 For each k ≥ 1letS k be the set of composite objects defined by S k = {(T,N):T ∈C k and N ∈N |T| }, where as before N is the set of height ... [5]. Zeilberger gave a q-Foata proof of the q-Pfaff-Saalsch¨utz identity [20], inspired by Foata’s bijective proof of the Pfaff-Saalsch¨utz identity [6]. In view of the fact that...

Ngày tải lên: 07/08/2014, 06:22