Báo cáo toán học: "On Zeilberger’s Constant Term for Andrews’ TSSCPP Theorem" ppsx

... r ed ucing a constant term in 2k variables to a constant term in k variables. As applications, Zeilberger’s constant terms are converted to single determinants. The result extends for two classes ... Jacobi’s Change of Variable Formula We first complete the proof of Identity 2 by transforming the constant term into known constant terms. Here, we mean Macdonald’s constant...

Ngày tải lên: 08/08/2014, 14:23

... = n  k=0  N(k, I) − N(k, J)  w k (T ). (2.4) We need the explicit formula for the case i 1 = 0 for our calculation. As stated in [8], the formula for this case can be derived using an action π on Laurent ... can solve for A T such that the constant term of  T A T x v 1 ···x v l x u 1 ···x u l D n (x, a, q) has the desired cancelations. However, experiments show that there is...

Ngày tải lên: 08/08/2014, 14:23

... Furthermore, we derive formulas for the generating functions for the numbers u(4n), u(4n + 1), u(4n + 2) and u(4n + 3), which are analogous to the generating function formulas for the partition functions ... combinatorial interpretations for t(n) and u(n) in terms of hooks of even length. 2 The generating function formula In this section, we shall derive a generating function formula...

Ngày tải lên: 08/08/2014, 11:20

... Guo [1] gave another proof for Yang’s formula. The objective of this paper is to give combinatorial proofs of Yang’s formula for k-ary trees and the other formula of Han for binary trees. Recall ... Yang’s formula for k-ary trees and the other formula of Han for binary trees. Our bijections are based on the structure of k-ary trees associated with staircase labelings. Keywords: hook...

Ngày tải lên: 08/08/2014, 14:23

... 1.2 For any sequence of the form (2), there exists a positive integer N such that a k − a k−1 ∈ P 1 for every k > N. Actually in [4] this conjecture is stated for starting values of the form ... for the first time for k = 66, which corresponds to c 4 = 2r 4 − 1. But neither r 4 = 66 nor c 3 = 99 are prime. 2 Relation between the conjectures We start by giving the alternative formu...

Ngày tải lên: 08/08/2014, 14:23

Ngày tải lên: 05/08/2014, 10:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

Ngày tải lên: 05/08/2014, 15:21

... Λ p is the E 1 -term of the Adams spectral sequence of spheres for p an odd prime, whose E 2 -term is Ext ∗ A(p) (F p , F p )where A(p) denotes the mod p Steenrod algebra, and E ∞ -term is a graded ... dΦ(λ n−1 ), for any n ≥ 1. Similarly, we obtain Φ(δ(μ n−1 )) = dΦ(μ n−1 ), for any n ≥ 0. So Φ is an isomorphism of differential algebras. The theorem is proved.  4. An Additive Bas...

Ngày tải lên: 06/08/2014, 05:20