Báo cáo toán học: "Franklin’s argument proves an identity of Zagier" pdf

... which, miraculously, Franklin’s argument proves at once. The author wishes to thank George Andrews and Don Zagier for supplying him with copies of [3] and [8], and also an anonymous referee for ... [1] and presented in more detail in [8]. Zagier [8] deduces (2) from (8), essentially by carefully differentiating with respect to x and setting x =1. Franklin’s argument proves an id...

Ngày tải lên: 07/08/2014, 06:22

... rev(r[max, v](σ)). Proof. Let m = majcode(σ) and r[max, v](σ) = r 1 . . . r k . Recall that 1  r 1 < r 2 < · · · < r k = n and r i is gr eater than any element of σ on the right of r i . Let ... 17. [10] P.A. MacMahon, The indices of permutations and derivation therefrom of functions of a single variable associated wi th the permutations of any assemb l age of objects,...

Ngày tải lên: 08/08/2014, 12:22

... edge-connectivity of cages Ping Wang 1∗ Baoguang Xu 2 Jianfang Wang 2 1 Department of Mathematics, Statistics and Computer Science, St.Francis Xavier University, Antigonish, NS, Canada, B2G 2W5, 2 Institute of ... smaller cycle of G  to denote any cycle of G  having length less than g. ∗ Research supported by the Natural Sciences and Engineering Research Council of Canada the el...

Ngày tải lên: 07/08/2014, 07:21

... e x and e y , joining x and y  , y and x  , respectively. Definition 2.2 Let G be a graph, let (D, f) be a 3-flow of G and let F ⊆ E(G)\supp(f). A3-flow(D  ,f  ) of G is called an (F, f)-changer ... 3-flow of G and H be a subgraph of G (1). If H ∼ = W 4 and e ∈ E(H) \ supp(f) is a center edge, then an ({ e},f)-changer exists. (2). If H is a circuit of length 3 with E(H) ∩ supp(f...

Ngày tải lên: 07/08/2014, 07:21

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Ngày tải lên: 05/08/2014, 15:20

... For any prime p ≡ 5 or 11 (mod 12), the coefficient of q pn−(p+1)/2 in 1 (q) p−4 ∞ ∞  n=0  2n n  q n 5 3. Modular Forms. Ramanujan, Ewell, Gandhi (and probably many others) have proved instances of ... =7,a=b=1,c 7 (1, 1) = 2,α m =1ifm≥0, and 0 if m<0, we see that V 7m+5 ≡ 0(mod7). 4 RAMANUJAN’S METHOD IN q-SERIES CONGRUENCES by George E. Andrews (1) and Ranjan Roy Written in honor o...

Ngày tải lên: 07/08/2014, 06:22

... tilings of the plane by triangles and create patterns by decorating the triangles, but these were not equilateral triangles. His focus of that investigation was not patterns, but rather the number of different ... rotations of the translation block. Case Ca consists of all signatures that use aspects 1, 2, and 3, case Cb consists of those that use aspects 2, 3, and 4, and for...

Ngày tải lên: 07/08/2014, 06:22

... members of C(n) and those of B(n), such that weight(S([π, σ])) = −weight([π, σ]). Hence the weights of the bad members of B(n) and C(n) cancel each other in pairs, contributing a total of zero ... and σ is a matching of {2, . . . , n} to {2  , . . . , n  }, and define the weight similarly. Let C(n) be the set of pairs [π, σ], where now n and 1  are unmarried and 1 and n  don’...

Ngày tải lên: 07/08/2014, 06:22

... Frankl, and R. Stanley, The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem, Combinatorica, 7 (1987), pp. 23–34. [4] A. Bj ¨ orner, A. Garsia, and R. Stanley, ... to an improved proof of Proposition 2.3. the electronic journal of combinatorics 8 (2001), #R11 18 Dumont’s statistic on words Mark Skandera Department of Mathematics University o...

Ngày tải lên: 07/08/2014, 06:22