Báo cáo toán học: "A Combinatorial Proof of the Sum of q-Cubes" pptx

... consideration of Contact Committee of the Heads of the SAIs of the European Union Luxembourg, 6 – 7 December 2004 (version 29 October 2004) based on education, training and experience, of ... finalisation of these Standards. The amended version was sent to EU SAIs and discussed at the Liaison Officers Meeting on 4-5 October. In conc...

Ngày tải lên: 06/03/2014, 23:20

... v(G) denote the number of vertices, and (G) denote the number of edges. In this paper, we construct a graph G having no two cycles with the same length which leads to the following result. Theorem. ... Chunhui Lai, On the size of graphs with all cycle having distinct length, Discrete Math. 122(1993) 363-364. [6] Chunhui Lai, The edges in a graph...

Ngày tải lên: 07/08/2014, 06:22

... 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

... is the number of times the integer i occurs in the sequence T . Note that the sum of all b(i), 1 ≤ i ≤ n,isequaltol, the length of T . 3 A simple proof for the existence of exponentially balanced ... two, or are two successive powers of two. A proof for the existence of exponentially balanced Gray codes is derived. The proof is much sim- p...

Ngày tải lên: 07/08/2014, 08:22

... 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

... agree above row r and to the left of column c (and the definitions of r and c) we see that the only possibility for /à is (r, c), completing the proof of this case and the theorem. Acknowledgements. ... 308, 9 (2008), 1524–1530. the electronic journal of combinatorics 15 (2008), #N23 4 A sharp bound for the reconstruction of partitions Vincent Vatter Departme...

Ngày tải lên: 07/08/2014, 15:22

... interpretation of the closed formula (10) for the number of con- vex permutominoes. We remark that the expression of f n resembles the expression (1) for the number c n of convex polyominoes of semi-perimeter ... : the uppermost cell of the rightmost column of the polyomino has the maximal ordinate among all the cells of the polyomino; U2 :...

Ngày tải lên: 07/08/2014, 15:22

... 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

... 2 n−1  k=1 k Cov  f, T (k) f  , (14) the electronic journa l of combinatorics 17 (2010), #R168 11 A probabilistic approach to the asymptotics of the length of the longest alternating subsequence Christi ... the lines of the previous section, re- lating the counting of maxima to the length of the longest alternating subsequence and then,...

Ngày tải lên: 08/08/2014, 12:23

... a short proof for the result of Noonan [3] that the number of permutations of length n containing exactly one occurence of pattern 321 is 3 n  2n n−3  . (To be precise, Noonan considered permutations ... A short proof for the number of permutations containing pattern 321 exactly once Alexander Burstein Department of Mathematics Howard...

Ngày tải lên: 08/08/2014, 14:23

... bias with tight limits of agreement. These Review Bench -to- bedside review: The importance of the precision of the reference technique in method comparison studies – with specific reference to the ... (OD) ultrasound techniques as a measurement of cardiac output. They compared these against ITD cardiac output from the pulmonary artery c...

Ngày tải lên: 13/08/2014, 11:23