Báo cáo toán học: "Area distribution and scaling function for punctured polygons" potx

... ∞. References [1] Madras N and Slade G 1993 The Self-Avoiding Walk (Boston: Birkh¨auser) [2] Hughes B D 1995 Random Walks and Random Environments, Vol I Random Walks (Oxford: Clarendon) [3] Vanderzande C 1998 ... quite straight-forward to generalise the algorithm to count twice punctured staircase polygons and in this case we obtained the series to perimeter 502 for k = 0, perimeter...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 05/08/2014, 15:21

... ∈ [n], we include arcs between i and j and between −i and −j if π contains e i −e j , an arc between i and −j if π contains e i + e j and arcs between i and 0 and between the electronic journal ... partitions. From now and on we choose Φ and Φ + explicitly as in [10, 2.10], so that positive roots are of the form e i ,2e i and e i ± e j for i<j, where the e i denote st...

Ngày tải lên: 07/08/2014, 06:22

... ratios, and a combinatorial formula for partitions of a polygon, for permanent preponderance, and for nonassociative products, Bull. Amer. Math. Soc., 54 (1948), 352–360. [21] R. Simion and W. ... 663–675. [2] J. Bandlow, Eric S. Egge and K. Killpatrick, A weight-preserving bijection between Schr¨oder paths and Schr¨oder permutations, Ann. Combin., 6 (2002), 235–248. [3] J. Ba...

Ngày tải lên: 07/08/2014, 07:21

... perfect Hilbertian basis for the group of even signed permutations D n . Proof. By Theorem 3.3 and Remark 3.2, a, b and d are perfect bases for S n = G(1, 1, n), B n = G(2, 1, n) and D n = G(2, 2, n), ... Biagioli and F. Caselli, Invariant algebras and major indices for classical Weyl groups, Proc. London Math. Soc. 88 (2004), 603–631. [6] R. Biagioli and F. Caselli, A desce...

Ngày tải lên: 07/08/2014, 15:23

Ngày tải lên: 05/08/2014, 15:21

... sufficient to prove that the formula holds for f(t)=e tx : If the formula is true for f(t)=e tx , then comparing coefficients of x n /n!on both sides we get that the formula holds for f (t)=t n . But this ... generating function for vertex-rooted trees and n − 1 times in the generating function for edge-rooted trees. Thus the difference w 3 z − 9w 4 z 2 /2 counts every unrooted tre...

Ngày tải lên: 07/08/2014, 13:21

... 1. Proof. For x ∈ X let G ∗ x = Sym(Fix(˜x)) and let X x = x G ∗ x . Consider the graph Γ with vertices {X x | x ∈ X} and edges {X x , X y }, for x, y ∈ X, whenever there exist v ∈ X x and w ∈ ... where Supp(x i ) = Supp(y i ) for 1 ≤ i ≤ m. Suppose that x i and y i differ by an odd number of simple transpositions for 1 ≤ i ≤ t and by an even number of simple transpositions...

Ngày tải lên: 07/08/2014, 21:21

... For the second case, deliberate clipping makes an intentional noise which falls both in-band and out-of-band. In-band distortion results in an error per- formance degradation, while out-of-band ... continuous Gaussian, and the PD is a function of m,wherem Î {0, 1 , N -1}.We provide a general form of the PD for m Î {0, 1 , N - 1}, and also derive the PD for exemplary cases of m ∈...

Ngày tải lên: 20/06/2014, 21:20

... generating functions for classical Weyl groups and affine Weyl groups. This section (and the remainder of the paper) is devoted to specializing Theorem 4 to compute generating functions for descents and ... method for computing the q-Eulerian distribution W (t, q)= w∈W t des(w) q l(w) as a rational function in t and q,where(W, S) is an arbitrary Coxeter system, l(w) is the leng...

Ngày tải lên: 07/08/2014, 06:20