Báo cáo toán học: "A note on three types of quasisymmetric functions" docx

... Classifications: 05E99, 16S34 Abstract In the context of generating functions for P -partitions, we revisit three flavors of quasisymmetric functions: Gessel’s quasisymmetric functions, Chow’s type B quasisymmetric ... on the set of all compositions of n by reverse refinement. The covering relations are of the form (α 1 , ,α i + α i+1 , ,α k ) ≺ (α 1 , ,α i ,α i+1 , ,α k ). L...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:21

... subsets of [1,n] are contained in arithmetic progression r mod ρ, where (k − )r ≡ 0modρ. If d  >ρthen every progression r mod d  consists of at most n/(ρ +1) elements hence it contains ... result of this note says that if (k − )/ is small in terms of ρ, then the number of (k, )-sum-free subsets of [1,n]isequalto(ϕ(ρ)+ϕ r (ρ)+o(1))2 n/ρ , where ϕ r (x) denotes the n...

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

... bipartite digraphs, namely, specifying conditions on the cardinality of the edge-set of the digraph that guarantee the existence of a directed simple cycle of length at most four. As usual in Tur´an ... ,m 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...

Ngày tải lên: 07/08/2014, 06:23

... (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 for basic ... in honor of Gian-Carlo Rota, Birkauser, Basel. 1998, pp. 111-129 [3] Z. G. Liu, Some operator identities and q-series transformation formulas, Discrete Math. 265(2003), 119-139. the electro...

Ngày tải lên: 07/08/2014, 08:22

... 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 |≥3, ... both transitive. the electronic journal of combinatorics 13 (2006), #N3 2 A Note on the Number of Hamiltonian Paths in Strong Tournaments Arthur H. Busch Department of Mathematic...

Ngày tải lên: 07/08/2014, 13:21

... hereditary class of graphs has index 1 if and only if it contains none of the three listed classes. The classes of index 1 have been called in [2] unitary. The family of unitary classes is of sp ecial ... n-vertex composition of k strips. The strips define an ordered partition of V into k nonempty subsets. We fix this partition and estimate the number of ways to compose G base...

Ngày tải lên: 08/08/2014, 14:23

... Teams for Innovation in the Construction of Talent Highlands in Guangxi Institutions of Higher Learning ([2011]47), and the support program of Key Laboratory of Spatial Information and Geomatics ... Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/ For information about other SpringerOpen publications go to http://www.springeropen.com Journal...

Ngày tải lên: 20/06/2014, 21:20

Ngày tải lên: 05/08/2014, 10:20