Báo cáo toán học: "A note on the number of edges guaranteeing a C4 in Eulerian bipartite digraph" pot

... E}.Since no directed C4contains v∗as a vertex, we must have that every w ∈ A appears in atleast one of A −or A +(it may appear in both; in particular, v∗appears in both A −and A +as there ... A note on the number of edges guaranteeing a C4 in Eulerian bipartite digraphsJian ShenDepartment of MathematicsSouthwest Texas State UniversitySan Marcos, TX 78666email: js48@swt.eduRaphael ... to [1]. In this paper we consider the most basic Tur´an-type problem in bipartite digraphs, namely, specifying conditions on the cardinality of the edge-set of the digraph that guarantee the existence...

Báo cáo toán học: "Improved bounds for the number of forests and acyclic orientations in the square lattice" doc

... the same way, an acyclic orientation on a fan graph induces an acyclic orientation on the corresponding comb graph. A simple adaptation of the last proof also gives a proof of the following the ... asmentioned before, the evaluation of the Tutte polynomial at these points is #P-hard forplanar bipartite graphs [11] and even for grid graphs of maximum degree 3 [12]. The approach for obtaining the ... generate the matrices Dkand Dkforsmall values of k.Weusematlab to obtain the corresponding eigenvalues. Here the note of the last section applies and we consider these eigenvalues accurate...

Báo cáo khoa học: "Shallow parsing on the basis of words only: A case study" pptx

... types of input. Second, there are indications thatincreasing the training set of language processingtasks produces much larger performance gains thanvarying among algorithms at ﬁxed training ... Task representation and evaluation methodTo formulate the task as a machine-learnable classi-ﬁcation task, we use a representation that encodes the joint task of chunking and function-tagging ... on the basis of POS informationalone, whereas the second module, the attacher,also uses lexical information. Chunks as a sepa-rate level have also been used in Collins (1996) andRatnaparkhi...

Báo cáo toán học: "Improved bounds on the length of maximal abelian square-free word" pot

... left-maximal if, for every a ∈ Σk,thewordaw contains an abeliansquare subword beginning with the initial a. In particular, an abelian square-free wordw is left-maximal over Σkif aw contains an ... certainly contains a 3, two 4’s, two 5’s, two 6’s and a 7. It may alsocontain up to two 2’s, up to two additional 3’s, and an additional 7. Even if it containedall of these, however, the last ... the letter i appears at least twice in the second half of sk−1,namelyonce in wiand once in wi+1, but sk−1is an abelian square, so i must also appear at leasttwice in the ﬁrst half of...

Báo cáo toán học: "Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap" potx

... simple proof of this last assertion, based on the decomposition of th e Laplacian of Cayley graphs, into a direct sum of irreducible representationmatrices of the symmetric group.1 IntroductionIf ... {1}, Z) the Cayleygraph of G associated to the generating set Z. If A Gis the adjacency matrix of G and ∆G the corresponding Laplacian, since G is |Z|–regular (counting loops), we have∆G= ... statement, namely for bipartite graphs,was also conjectured in [5]. Several papers have app eared with proof s of Aldous’s con-jecture for some particular classes of graphs, and recently a...

Báo cáo toán học: "General results on the enumeration of strings in Dyck paths" ppt

... generating functions.Finally, in Section 6, we unify the main results of Sections 3, 4 and 5.We note that some of the results of t his paper have been announced in the 7 th Inter-national Conference ... distinctionbetween these two not io ns. The le ngth |α| of a path α is the number of its steps. The height of a point of a path is its y-coordinate. A Dyck path is a path that starts and ends at the same height ... will also need the g enerating function A p(resp. Bs) of the set of all Dyck pathshaving preﬁx p (resp. suﬃx s), as well as the generating function Γp,s of the set of allDyck paths having...

Báo cáo hóa học: " Research Article On the Stability of Generalized Additive Functional Inequalities in Banach Spaces" pdf

... Rassias, On the stability of the linear mapping in Banach spaces,” Proceedings of the AmericanMathematical Society, vol. 72, no. 2, pp. 297–300, 1978.5 P. G˘avrut a, A generalization of ... M. Rassias, On the stability of functional equations and a problem of Ulam,” Acta ApplicandaeMathematicae, vol. 62, no. 1, pp. 23–130, 2000.16 Th. M. Rassias, Functional Equations, Inequalities ... Cauchy diﬀerence by a general control function in the spirit of Rassias’ approach.Rassias 6 during the 27th International Symposium on Functional Equations asked the question whether such a...

Báo cáo toán hoc:"Generating functions for the number of permutations with limited displacement." ppsx

... proofs in [3] were based on expanding a permanent. It was pointed out by one of the r eferees that the transfer-matrix method gives a more direct and elegant proof of the generating function. ... 1for the second transfer-matrix method, and that the matrix in the second transfer-matrixmethod is smallest possible for any transfer-matrix for this pro blem. the electronic journal of combinatorics ... z5 the electronic journal of combinatorics 16 (2009), #R104 9where v(n) is the number of closed walks of length n based at A 0. We claim that eachsuch walk is in bijection with a permutation...

Báo cáo toán học: "A note on the number of (k, )-sum-free sets" potx

... the electronic journal of combinatorics 7 (2000), #R30 3d (A) =gcd (A) ,d (A) =d (A − A) ,Λ (A) =maxA − minA, Λ (A) =Λ (A) /d (A) .Furthermore, letκ (A) =Λ (A) − 1 |A| −2,θ (A) =max (A) Λ (A) ,T ... Using an a netransformation of variables his theorem can be stated as follows.Theorem 1. Let A be a ﬁnite set of integers and let h be a positive integersatisfying h>2κ − 1. Then there ... (A) =( |A| −2)(κ (A)  +1− κ (A) ) + 1andhA = {a 1+ ···+ a h: a 1, ,a h∈ A} .For a speciﬁed set A, we simply write d, d, Λ, etc.Our approach is based on a remarkable result of Lev [7]. Using...

Báo cáo toán học: "A Note on the Number of Hamiltonian Paths in Strong Tournaments" ppsx

... paths thatinclude the arc vn→ v1, and there is a unique hamiltonian path of T that avoids this arc.Hence, there are 2n−2+ 1 distinct hamiltonian paths in a nearly transitive tournament of order ... R.Proof. Note that we allow the special case where m = 0; in this case the path Q is a path on 0 vertices, and R = P satisﬁes the lemma trivially. The remainder of the proof is by induction on ... repeat the above argument with the portion of Rbeginning at um−1and the vertex um.Theorem 1. Let hp(n) be the minimum number of distinct hamiltonian paths in a strongtournament of order...

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