Báo cáo toán học: "A Binomial Coefficient Identity Associated with Beukers’ Conjecture on Ap´ry numbers e" docx

... A Binomial Coefficient Identity Associated with Beukers’ Conjecture on Ap´ery numbers CHU Wenchang ∗ College of Advanced Science and Technology Dalian ... Classifications: 05A19, 11P83 Abstract By means of partial fraction decomposition, an algebraic identity on rational function is established. Its limiting case leads us to a harmonic number identity, which ... turn has...

Ngày tải lên: 07/08/2014, 08:20

Ngày tải lên: 07/08/2014, 06:22

... Laurent monomials in u with positive coefficients. Thus, applying π to this expansion, x = π(X P w [m+1] ) is a linear combination of Laurent monomials in (x 1 , x 2 ) with positive coefficients. Similarly, ... combination of Laurent monomials in (x 1 , x 2 ) with positive coefficients. This proves the theorem. Example 9. We consider the cluster algebra A(2, 3) with initial cluster (x 1 , x...

Ngày tải lên: 08/08/2014, 01:20

... the electronic journal of combinatorics 5(1998), #R3 4 2 The construction Let n, a parameter of our construction, be some integer greater than 1. We con- struct an infinite dimensional difference ... 2 n−1 . In 1931 Erd˝os conjectured that this is not the case [E1]. In particular, he conjectured that f(n) ≥ c2 n for some constant c, and he offered $500 for settling this conjecture [E1] [G1] [G...

Ngày tải lên: 07/08/2014, 06:22

... complexes along with the basic operations defined for them. Section 4 encodes productions as Boolean complexes and relates operations on graphs with operations on Boolean complexes. Section 5 studies ... p 1 (restrictions on p 2 actions due to p 1 ) and p 3 ; p 2 (restrictions on p 3 actions due to p 1 ) and or them. Finally, we have to deduce which conditions have to be imposed o...

Ngày tải lên: 07/08/2014, 21:21

... 2k  q , where  n k  q stands for the q -binomial coefficient. We provid e two proofs, one of which is comb inatorial via partitions. 1 Introduction Using the Lagra nge inversion fo r mula, Mansour and Sun ... Mar 31, 2011 Mathematics Subject Classifications: 05A10, 05A17 Abstract We give a q-analogue of some binomial coefficient identities of Y. Sun [Electron. J. Combin. 17 (2010), #N20]...

Ngày tải lên: 08/08/2014, 14:23

... functions, q,t-Kostka coefficients Abstract The two parameter family of coefficients K λµ (q, t) introduced by Macdonald are conjectured to (q, t) count the standard tableaux of shape λ. If this conjecture ... of horizontal strips of size k by H k so that the notation λ/µ ∈H k means that λ/µ is a horizontal strip with k cells. Similarly, the class of vertical strips (skew partitions with on...

Ngày tải lên: 07/08/2014, 06:22

... follows. Section 2 contains the definitions and notation about partitions needed in this paper. In Section 3 we give the proof of the main theo- rem. Section 4 deals with the Kronecker coefficient k(λ, ... Applications We conclude this paper with an application to the expansion of χ µ ⊗ χ ν when ℓ(µ) = 2 = ℓ(ν). It is well known that any component of χ µ ⊗ χ ν corresponds to a partition of...

Ngày tải lên: 07/08/2014, 21:21

... Classifications: 05A30, 33D70 Abstract In this paper, we introduce a direct method to evaluate the Dyson coefficients. 1 Introduction In 1962, Dyson [2] conjectured the following constant term identity. Theorem ... in evaluating the coefficients of monomials M : =  n i=1 x b i i , where  n i=1 b i = 0, in the Dyson product. Based on Good’s proof, Kadell [6] gave three non-constant term coeffic...

Ngày tải lên: 08/08/2014, 11:20

... based on the full status elements: speed difference, location, and direction rather than considering only position and direction. Some clustering techniques took mobility into consideration for ... decisions before entering the crash dangerous zone [4, 5]. Moreover, information about the current transportation conditions facilitate driving by taking new routes in case of congestion, thus .....

Ngày tải lên: 20/06/2014, 20:20