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

... is (k, )-sum-free for k,  ∈ N, k>,ifthereare no solutions to the equation x1+ ···+ xk= y1+ ···+ yin A. Denoteby SFnk, the number of (k, )-sum-free subsets of [1,n]. Since the ... ρ). The main 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)+ϕr(ρ)+o(1))2n/ρ,where ϕr(x) denotes the ... com-ments. Due to their suggestions we were able to prove the main result of the note in its present sharp form. the electronic journal of combinatorics 7 (2000), #R30 2odd numbers is (2, 1)-sum-free...

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

... bipartite digraphs, namely, specifying conditions on the cardinality of the edge-set of the digraph that guarantee the existence of a directed simplecycle of length at most four. As usual in Tur´an ... columnsj =1, ,ρn.DenotebyM4 the block consisting of the rows i = |A+|+1, ,mand the columns j =2ρn+1, ,n.DenotebyM5 the block consisting of the rows i =1, ,|A+|and the columns j =2ρn +1, ,n. ... visualizes these terms.Let c(s, k) denote the number of entries of M equal to k in the block Msfor s =1, 2, 3, 4, 5andk = −1, 0, 1. For normalization purposes, deﬁne f(s, k)=c(s, k)/mn.Consider the...

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

... not strong and that nosets A and B satisfy the lemma. Let t be the number of strong components of T − vand let Wibe the set of vertices in the ithstrong component. If |W1|≥3, then choosea ... v1and all other arcs are of the form vi→ vjwith i<j. In other words,reversing the arc vn→ v1gives the transitive tournament of order n. As noted by Moon[1], there is a bijection between ... whichsatisfy the lemma. So we can assume that T [W ] and hence T − v are both transitive. the electronic journal of combinatorics 13 (2006), #N3 2A Note on the Number of Hamiltonian Paths inStrong TournamentsArthur...

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 ranks of set-inclusion matrices" pps

... 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, let W = Wt,k(v) be the (0,1)-matrix of inclusionsfor ... A note on the ranks of set-inclusion matricesD. de CaenDepartment of Mathematics and StatisticsQueen’s UniversityKingston, Ontario, Canada K7L 3N6decaen@mast.queensu.caSubmitted: ... ﬁeld, and let rF(M) denote the rank of M over F .Theorem. If (k − t) =0intheﬁeldF ,thenrF(Wt,k(v +1))=rF(Wt,k−1(v)) + rF((k − t +1)Wt−1,k(v)). (1)Proof. The block-matrix identityI...

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

... vertices,which is the main result of the paper. The o r ganization of the paper is as follows. In the rest of this section we introduce basic notations. In Section 2, we verify the conjecturefor ... is the intersection graph of a set I = {I1, . . . , In} of intervals (arcs) on a circle C, i.e. if there exists a one-to-one correspondence between the vertices of Gand the intervals of ... k). Note that k ≤ n, since each strip adds at least one vertex to the resulting graph. Wedenote the number of vertices in the i-th strip by ni= ti+ 2, where tiis the number of vertices the...

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

... the condition nP(|X1| > ηn) ≤ c(log n)ε0, 0 < ε0< 1 in theorem 1.1 of [12].Remark 1.4. If EX2< ∞, then X is in the domain of attraction of the normal law. Therefore, the ... of random variablesin the domain of attraction of the normal law, we will show that the ASCLT holds under a fairly general growthcondition on dk= k−1exp(ln k)α), 0 ≤ α < 1/2.Our theorem ... weights. On the other hand, by the Theorem 1 of Schatte [3], Equation (3) fails for weight dk= 1. The optimal weightsequence remains unknown. The purpose of this article is to study and establish the...

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

... 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 the ... the reﬂection representation of a ﬁnite Coxetergroup. This is essentially what we are looking at. (The deﬁning representation of Snconsists of the direct sum of the reﬂection representation ... table. By the preceeding lemma, the Nthentry of the column corresponding to the λ-cycles is equal to the number of nonnegative integer solutions to the equation λ1x1+ ···+ λkxk= N.Consequently,one...

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

... conditioning on the event CP0, the random graphs of the resulting probabilityspace may contain edges only from within the edges that connect vertices of diﬀerentpartitions of P0. The number ... information on Maple) implementation of the downhill simplex function optimizationmethod (see [13] for a good description of the method and a C implementation) to the maximize the expression. This ... make the connection with the problem of placing uniformly atrandom a number of balls into a number of bins (for a thorough treatment of suchproblems, see [11]). After the rn edge selections, the...

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

... bounded, then the height distributionconcentrates on two consecutive points.3 Derivation of ResultsWe establish the ﬁve parts of Theorem 2. Since the analysis involves a routine use of the saddle ... of k. For purposes of comparison, we repeat these results below.Theorem 1 The distribution of the height of b-tries has the following asymptotic expan-sions for ﬁxed b:(i) Right-Tail Region: ... shallprove that in the region where most of the probability mass is concentrated, the height the electronic journal of combinatorics 7 (2000), #R39 5where x is the fractional part of x,thatis,x...

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