Báo cáo toán học: " COMBINATORIAL PROOFS OF CAPELLI’S AND TURNBULL’S IDENTITIES FROM CLASSICAL INVARIANT THEORY" potx

... d j    = G  . COMBINATORIAL PROOFS OF CAPELLI’S AND TURNBULL’S IDENTITIES FROM CLASSICAL INVARIANT THEORY BY Dominique FOATA ∗ and Doron ZEILBERGER ∗∗ 0. Introduction. Capelli’s [C] identity ... Kostant and Sahi [K-S] discovered and proved an anti-symmetric analog of Capelli’s identity. Although we, at present, are unable to give a combinatorial proof sim...

Ngày tải lên: 07/08/2014, 06:20

... identity in combinatorial analysis, Proc. Glasgow Math. Ass. 5 (1961), 197-200. [28] P. Paule, Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type, ... Band, G. Reimer, Berlin, 1881. [24] S. Kongsiriwong and Z. G. Liu, Uniform proofs of q-series-product identities, Results in Math. 44 (2003), 312-339. . [25] R. P. Lewis,...

Ngày tải lên: 07/08/2014, 13:21

... acceptance. Fully formatted PDF and full text (HTML) versions will be made available soon. New proofs of Schur-concavity for a class of symmetric functions Journal of Inequalities and Applications 2012, ... t)y j ) 2   2 ≤ 0, and then h  (t) ≤ 0, so f (t) is concave on (0, 1). NEW PROOFS OF SCHUR-CONCAVITY FOR A CLASS OF SYMMETRIC FUNCTIONS HUAN-NAN SHI ∗ , JIAN ZHANG...

Ngày tải lên: 20/06/2014, 21:20

... bijective proofs, such as the Gessel–Viennot method [4, 5] of nonintersecting lattice paths in Remmel’s proof [10], and the probabilistic proof [6] by Greene, Nijenhuis and Wilf in Zeilberger’s proof ... r.The components of λ are called the parts of λ. The integer n, the sum of all the parts of λ, is called the norm of λ and is denoted by n(λ). The (ordinary) Ferrers diagra...

Ngày tải lên: 07/08/2014, 06:20

... adjacent, and thus forming afactorAB or BA. In the parentheses on the right-hand side of (6), the first summand accounts for those summands from T 2n+1,n that contain AB, while the second summand accounts ... first proof of (13) appears in [2]. It may be viewed as the first non- commutative extension of Euler’s evaluation of ζ(2n). Theorem 2 Let n be a positive integer, and let I d...

Ngày tải lên: 07/08/2014, 06:22

... 3.3 and 3.4 comprise the first steps of Bouc’s proof of Theorem 1.1. At this point our proof departs from Bouc’s and follows a path analogous to that of Friedman and Hanlon [4] for the chessboard ... each eigenvalue c and partition λ of n, the multiplicity of the irreducible S λ in the c-eigenspace of Λ n,r−1 equals the multiplicity of S λ  in the c-eigenspace of L n...

Ngày tải lên: 07/08/2014, 06:23

... certain class of binary trees and the set of colored 5-ary trees. The generalization of the parity reversing involution and the bijection to forests of colored binary trees and forests of colored ... of improper forests of colored binary trees, which reverses the parity of the color numbers of the forests. Hence the right side summand of Formula (1.1) counts the numb...

Ngày tải lên: 07/08/2014, 15:22

... elegant combinatorial proof of (4) was given by Shattuck [12], and a little complicated combinatorial proof of (2) was provided by Chen and Pang [5]. On the other hand, as a q- analogue of Sun’s ... i k  a s−i k (a 0 = +∞) and b k − i k becomes a part of λ and i k becomes a positive part of µ. 4 The proof of (5) By the inverse of Algor ithm Z, the relation (8) holds...

Ngày tải lên: 08/08/2014, 11:20

... find it from combinatorial theory of generating functions. Theorem 8. The integer V (n, k) is the number of partitions of [2n+1] into 2k +1 blocks of odd cardinality. Proof. This follows from the ... between the model of Dumont and that of Andrews and Littlejohn? • Thirdly, is there any combinatorial interpretation for the coefficient b (i) n,k in the Jacobi-Stirling numb...

Ngày tải lên: 08/08/2014, 12:22

... give “hybrid” proofs of the q-b inomial theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use ... replaced with aq). Analytic proofs were given by Watson [32] a nd Andrews [1], and a combinatorial proof has been given in [9] by Berndt, Kim and Yee. Theorem 3. If |q| <...

Ngày tải lên: 08/08/2014, 14:22