Báo cáo toán học: "A note on an identity of Andrews" docx

... B. E. Sagan, R. P. Stanley (Eds.), Mathematical Essays in honor of Gian-Carlo Rota, Birkauser, Basel. 1998, pp. 111-129 [3] Z. G. Liu, Some operator identities and q-series transformation formulas, ... (13) The proof is completed. References [1] G.E.Andrews,Ramanujan’s ”lost” notebook. I. Partial θ-functions, Adv. in Math. 41 (1981), 137-172 . [2] W.Y.C.Chen-Z.G.Liu,Parameter augmentation f...

Ngày tải lên: 07/08/2014, 08:22

Ngày tải lên: 05/08/2014, 15:21

... k>,ifthere are no solutions to the equation x 1 + ···+ x k = y 1 + ···+ y  in A. Denote by SF n k, the number of (k, )-sum-free subsets of [1,n]. Since the set of 1 the electronic journal of combinatorics ... representation by sumsets and subset sums, J. Num- ber Theory 62 (1997), 127–143. the electronic journal of combinatorics 7 (2000), #R30 6 Observe that H is increasing...

Ngày tải lên: 07/08/2014, 06:20

... A note on the ranks of set-inclusion matrices D. de Caen Department of Mathematics and Statistics Queen’s University Kingston, Ontario, Canada K7L 3N6 decaen@mast.queensu.ca Submitted: ... relation is derived for the rank (over most fields) of the set-inclusion matrices on a finite ground set. Given a finite set X of say v elements, let W = W t,k (v) be the (0,1)-matrix of inclus...

Ngày tải lên: 07/08/2014, 06:22

... and j = ρn +1, ,2ρn.Denotethisblock M 2 .DenotebyM 3 the block consisting of the rows i = |A + |+1, ,m and the columns j =1, ,ρn.DenotebyM 4 the block consisting of the rows i = |A + |+1, ,mand ... holds if and only if both m and n are divisible by 3. Any graph demonstrating an equality must be biregular. Brualdi and Shen have shown in [3] how an upper bound for b(m, n) corresponds to...

Ngày tải lên: 07/08/2014, 06:23

... composition keeps track of both the set of signs and the set of descents of the permutation as we demonstrate with an example. If sC(π)=(−3, 2, 1, −2, 1), then we know that π is a permutation in ... Bergeron and C. Hohlweg, Coloured peak algebras and hopf algebras, arXiv: math.AC/0505612. [3] C. Bonnaf´e and C. Hohlweg, Generalized descent algebra and construction of irre- ducible...

Ngày tải lên: 07/08/2014, 13:21

... order n. As noted by Moon [1], there is a bijection between partitions of V \{v 1 ,v n } and hamiltonian paths that include the arc v n → v 1 , and there is a unique hamiltonian path of T that ... T − v is not strong and that no sets A and B satisfy the lemma. Let t be the number of strong components of T − v and let W i be the set of vertices in the i th strong component. If |W 1 |...

Ngày tải lên: 07/08/2014, 13:21

... set of intervals I of C, none including another, such that no point of C is an endpoint of more than one interval so tha t: (a) If two vertices u and v are adjacent, then φ (u) and φ(v) belong ... factorial i f and only if G is a non-trivial induced subgraph of P 4 . From now on, we assume that none of the forbidden graphs is an induced subgraph of P 4 . This leaves us with...

Ngày tải lên: 08/08/2014, 14:23

... Berkes and Cs ´ aki [7], H ¨ ormann [8], Wu [9, 10], and Ye and Wu [11]. Huang and Zhang [12] and Zhang and Yang [13] obtained ASCLT results for self-normalized version. Under mild moment conditions ... Foundation of China (11061012), the project supported by program to Sponsor Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20