Báo cáo toán học: "Generating functions attached to some infinite matrices" ppsx

... u s,s , are algebraic over F (z). the electronic journal of combinatorics 18 (2011), #P5 3 Generating functions attached to some infinite matrices Paul Monsky Brandeis University Waltham MA 02454-9110, ... automorphism of the splitting field that is the id e ntity on F (z) a nd permutes the roots that hav e positive ord among themselves. The goal of this section is to show that som...

Ngày tải lên: 08/08/2014, 12:23

... (ζ) Q(ζ) −xP (ζ) . Now Q(ζ) − xP (ζ) may be factored as C(x)  j  1 − D j (x)ζ  for some algebraic functions C(x)andD j (x), and it is not difficult to show that the D j must be distinct (since ... is well-known (and easy to prove) that  ζ n =1 R(ζx)=n  k r nk x nk . (3.1) In some cases, we have an explicit formula for r i that we can use, with the help of (3.1), to evaluate  ζ...

Ngày tải lên: 07/08/2014, 06:22

... step path from U {0,0} to U {0,0} will remove the first n r ows and the first n columns of A 0,0 . Hence, it corresponds to a permutation. To describe the path that corresponds to a given permutation ... these elements by ch a nging “∗” to “·” to show the h i s tory of the process, moreover, “◦” from previous steps are m arked by “•”). the electronic journal of combinatorics 16 (200...

Ngày tải lên: 08/08/2014, 01:20

... these give rise to a factor of q ( 2 2 ) + ( n−3 2 )  n−1 2  p,q . Thus the total contribution from case (i) to (5.6) is q 1+ ( n−2 2 ) p 2  n−1 2  p,q . In case (ii) n gives rise to n − 1 inversions ... each brick reading from left to right. We think of each such filling as a permutation of S n by reading the numbers in rows from top to bottom and the numbers from left to rig...

Ngày tải lên: 08/08/2014, 12:22

Ngày tải lên: 05/08/2014, 15:21

... per- muting operator on 3 , mapping a vector [x 1 ,x 2 ,x 3 ]to[ x 2 ,x 3 ,x 1 ]. In analogy with this, a -permutation π is going to be an operator on , mapping a vector [ ,x −1 ,x 0 ,x 1 ,x 2 , ]to[ ,x π −1 ,x π 0 ,x π 1 ,x π 2 , ... positions i. Proof The value on position π i is moved to position i by π and further to position i+n by T n ,thenontoπ i+n by π −1 and finally to π i+n...

Ngày tải lên: 07/08/2014, 06:22

... converges to a geometric distribution if i, j → ∞. the electronic journal of combinatorics 17 (2010), #R137 2 Remark 3 In the case of recursive trees, there is a simple relation to another combina- torial ... another similar bijection and use it to determine the distribution of the depth of the lowest common ancestor of two nodes i and j, i < j. It turns out (somewhat surprisingly) t...

Ngày tải lên: 08/08/2014, 12:22

... 1623– 1635. [4] K. Dilcher, Some q-series identities related to divisor functions, Discrete Math., 145(1995) 83–93. [5] A.M.FuandA.Lascoux,q-identities from Lagrange and Newton interpolation, Adv. Appl. ... Utilitas Math., 25(1984) 377–379. [10] J. Zeng, On some q-identities related to divisor functions, Adv. Appl. Math., 34(2005) 313–315. the electronic journal of combinatorics 12...

Ngày tải lên: 07/08/2014, 13:21

... involutory automorphism of K  associated with H and let K denote the fixed field of θ. Let (·, ·) denote a skew-θ-Hermitian form of a 3-dimensional vector space V over K  which gives rise to the ... for the Hermitian dual polar spaces to extend the original results to the infinite case. We first discuss the symplectic case. Let V be a 2n-dimensional vector space (n ≥ 2) over a field K eq...

Ngày tải lên: 07/08/2014, 15:22

... consequences of similar combinatorial formulas in the Yangian. The elementary symmetric functions in the Yangian of the Lie algebra gl n (C) are known to b e generators of Bethe subalgebra. Bethe ... commute. The relation to elementary symmetric functions is given by e k (u) = det (h − j− i+1 (u − j + 1)). One can go further and intro duce combinatorial analogues of Schur functions:...

Ngày tải lên: 08/08/2014, 01:20