Báo cáo toán học: " A note on the speed of hereditary graph properties" ppsx

... factorial.Corollary 3. The clas s of circular interval graphs and the class of l inear interval grap hsare fa ctorial.Proof. Corollary follows from the fact that both classes are subclasses of the class of circular ... that this class is a proper subclass of the class of circular arc graphs. A graph G is a circular arc graph if it is the intersection graph of a set I = {I1, . . . , In} of intervals (arcs) on ... representat io n is called a circ ular interva l graph. A special case of circular interval graphs are linear interval graphs which are deﬁned in the same way with C being a line instead of a circle.Fuzzy...

Báo cáo toán học: "A note on the space of pseudodifferential projections with the same principal symbol " pptx

... ...

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 ... 1 |A| −2,θ (A) =max (A) Λ (A) ,T (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 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...

Báo cáo toán học: "A note on the ranks of set-inclusion matrices" pps

... A note on the ranks of set-inclusion matricesD. de CaenDepartment of Mathematics and StatisticsQueen’s UniversityKingston, Ontario, Canada K7L 3N6decaen@mast.queensu.caSubmitted: ... be the (0,1)-matrix of inclusionsfor t-subsets versus k-subsets of X : WT,K=1ifT is contained in K, and 0 otherwise.These matrices play a signiﬁcant part in several combinatorial investigations, ... 11, 2001; Accepted: June 16, 2001Abstract A recurrence relation is derived for the rank (over most ﬁelds) of the set-inclusionmatrices on a ﬁnite ground set.Given a ﬁnite set X of say v elements,...

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

... 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 are no antiparallel ... 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 of a ... Hence, A − A += A. Thus, at least one of them hascardinality at least m/2. Assume, without loss of generality, that |A +|≥m/2(otherwisewe can reverse the directions of all edges and the result...

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

... 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 n.Lemma ... 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 m.Form ... other words,reversing the arc vn→ v1gives the transitive tournament of order n. As noted by Moon[1], there is a bijection between partitions of V \{v1,vn} and hamiltonian paths thatinclude...

Báo cáo toán học: " A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law" pptx

... unknown. The purpose of this article is to study and establish the ASCLT for self-normalized partial sums of random variablesin the domain of attraction of the normal law, we will show that the ASCLT ... article as it appeared upon acceptance. Fully formattedPDF and full text (HTML) versions will be made available soon. A note on the almost sure limit theorem for self-normalized partial sums of random ... the domain of attraction of the normal law. Therefore, the class of randomvariables in Theorems 1.1 is of very broad range.Remark 1.5. Essentially, the open problem should be whether Theorem...

Báo cáo toán học: "A Note on the Symmetric Powers of the Standard Representation of Sn" ppt

... A Note on the Symmetric Powers of the StandardRepresentation of SnDavid Savitt1Department of Mathematics, Harvard UniversityCambridge, MA 02138, USAdsavitt@math.harvard.eduRichard ... row-span of this table. Since the dimension of the row-span of a matrix isequal to the dimension of its column-span, we can equally well study the dimension of the space spanned by the columns of ... write all of the generating functions fλ(q) as rational functions over a common denominator; then the dimension of their span is bounded above by 1 plus the degree of their numerators.For example,...

Báo cáo toán học: "A note on the non-colorability threshold of a random graph" pot

... sharp estimates obtained by Kamath et al. of the probability that no bin is empty after the random placement of the ballsand exploiting the relationship between the placement of balls and the rigid ... special colorings that satisfy a maximality condition that, however, is a weaker form of maximality than the oneconsidered in [10]. This has as an eﬀect a smaller right-hand side in (1) that resultsin ... set the accuracy parameter equal to 10−50and set the scale of the problem equal to10−50. Finally, we set the number of decimal digits parameter of Maple equal to 100. Werun the algorithm and...

Báo cáo toán học: "A Note on the Asymptotic Behavior of the Heights in b-Tries for b Large" ppt

... depend on n. There are other applications of b-triesin computer science, communications and biology. Among these are partial match retrieval of multidimensional data, searching and sorting, pattern ... ﬁxed large b and n, the conditions under which (c)–(e) apply may notbe satisﬁed for any k. However, for a ﬁxed large b and k, we can always ﬁnd a range of nsuch that each of the parts of Theorem ... −hknand the approximations from Theorem 2, parts (a) and (b). The part (a) approximation is denoted by 1 − hkn (a) , etc. We see that when n = 17, (a) is a betterapproximation than (b),...

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