Báo cáo toán học: "q, t-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C2)n" doc
Báo cáo toán học: "q, t-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C2)n" doc
... c·ρ(n2)1, the electronic journal of combinatorics 18 (2011), #P158 21q, t-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C2)nKyungyong Lee∗Department of MathematicsUniversity ... d′2), and the x-coordinates of the points in D are non-negative, i.e. D ∈ D.Proof of Claim. We give the exact lower and upper bounds of the y-degree of D, and show that every integer between these ... minimal set of generators of the ideal I [10, §1]. There is a set of generators of the diagonal ideal I defined as follows.Denote by N the set of nonnegative integers. Let Dnbe the collection o f...
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Báo cáo hóa học: " q-Bernoulli numbers and q-Bernoulli polynomials revisited" docx
... 306-791, KoreaFull list of author information isavailable at the end of the articleAbstractThis paper performs a further investigation on the q-Bernoulli numbers and q-Bernoulli polynomials ... Acikgöz, Erdal and Araci derived some results by using Theorems 1-3. Hence, the other results are incorrect.Now, we redefine the generating function of q-Bernoulli numbers and polynomials and correct ... functions for the q-Bernoulli numbers and polynomials are shown.Mathematics Subject Classification (2000) 11B68, 11S40, 11S80Keywords: Bernoulli numbers and polynomials, q-Bernoulli numbers and polyno-mials,...
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Báo cáo toán học: "q-Eulerian polynomials and polynomials with only real zeros" potx
... consequence of Corollary 3. Furthermore, if the multiplicity of 0 as a zero of f is m0, then the multiplicity of 0 as a zero of F is also m0except m0= α = 0; if the multiplicity of −1 as a zero of ... multiplicity of the real zeros of f and F, which generalizes and unifies many known results, including the results of Brenti and Br and en about the q-Eulerian polynomials.1 IntroductionLet Sndenote the ... B´ona and R. Ehrenborg, A combinatorial proof of the log-concavity of the numbers of permutations with k runs, J. Combin. Theory Ser. A 90 (2000) 293–303.[3] P. Br and en, On linear transformations...
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Báo cáo toán học: "Two-stage allocations and the double Q-function" pdf
... choice for the ith team with the probability ai=mi/m,wherem = m1+ + mN.In the next section, using the generating function for the numbers µr,weobtainanexpectation of the random variable ... Consider, for example,an Internet voting on the theme: “Which of the N teams will win the world cup?”. Ifvoters don’t know anything about the teams, then they make a choice (particle) for eachteam ... words with the samehash value. The model of random equiprobable allocations of particles (hash values of differentinput words) into N cells (elements of B) is often used in the analysis of collision...
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Báo cáo toán học: "Outerplanar Crossing Numbers, the Circular Arrangement Problem and Isoperimetric Functions" doc
... The circular arrangement problem requires the placement of the vertices of the graph into equidistant positions on a circle of perimeter |V (G)| ,and minimizes the sum of lengths of paths on the ... solved in his thesis the circular arrangement problem for the hypercube, and Bezrukov and Schroeder [1], who showed that for trees the solutions for the linear arrangement problem and the circular ... o(1))n464 and equality is conjectured here [20]. Therefore, the lower bound for ν1in terms of edge forwarding index (37) is always better than the the lower bound for cr in terms of edge forwarding...
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Báo cáo toán học: "q-Identities related to overpartitions and divisor functions" potx
... Mecha-nization of the Ministry of Science and Technology, and the National Science Foundation of China. The second author is partially supported by the EC’s IHRP Program, within the Research Training ... q-identitiesofFuandLascouxprovedbytheq-Rice formula, QuaestionesMath., 27(2004) 391–395.[8] K. Uchimura, An identity for the divisor generating function arising from sortingtheory, J. Combin. Theory, ... HPRN-CT-2001-00272.References[1] G. E. Andrews, The Theory of Partitions, Cambridge University Press, (1984). the electronic journal of combinatorics 12 (2005), #R38 62. More generally, given two alphabets X and Y, the generating...
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Báo cáo toán học: "On some Ramsey and Tur´n-type numbers for paths a and cycles" doc
... Hence there mustbeapathoforderk − p + 2 joining x and y in graph G. Theorem 9 For odd integers k ≥ 5T(n, Ck)=w(n, k − 1),where k ≤ n ≤ 2k − 2.Proof. The last part of the thesis of Theorem ... b(v)andg(v) we denote the number of red, blue and green edges incident to v, respectively. The degree of vertex v will be denoted by d(v) and the minimum degree of a vertex of G by δ(G). The ... facts which are often used in the paper.Definition 1 The circumference c(G) of a graph G is the length of its longest cycle.Definition 2 The girth of a graph G is the length of its shortest cycle.Definition...
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Báo cáo toán học: "Information flows, graphs and their guessing numbers" pptx
... bits and n output bits, and where the depth of the circuitis in O(log(n)). For a detailed discussion and further survey of this class of problems and their link to communication complexity and ... shows that the information defect of the graphs G ∈˜Gn,d (and any shift s of those) is at mostn2−d2. For 1 > > 0 and for d = n the graphs in˜S are (for largevalues of n), sparse ... strategy so they all guess correctly if the sum of the dice valuesare 0 modulo s.Actually if the players know the sum of the dice values modulo s each player candeduce the value of their own...
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Báo cáo toán hoc:" q-Counting descent pairs with prescribed tops and bottoms" docx
... combinatorial proofs of a pair of formulas for PX,Yn,s.First of all, for any set A ⊆ N, letAn= A ∩ [n], and Acn= (Ac)n= [n] − A.Then Hall and R emmel [4] proved the following theorem.Theorem ... before it. So the number of ways to place xiis the difference between the sum of the number of +’s and the number of elements smaller than xiwhich are in Y , and the number of x ∈ X already placed, ... special cases, the formulas (1.6) and (1.7) can be significantly simplified. For example, we shall show that when Y is the set of natural numbers N and X is the set of even numbers 2N, thenPX,Y2n,s(q)...
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Báo cáo toán học: " Strong convergence theorems and rate of convergence of multi-step iterative methods for continuous mappings on an arbitrary interval" pptx
... newiteration, called the SP-iteration, and they proved the Mann, Ishikawa, Noor and SP-iterations are equivalent and the SP-iteration converges faster than the others for the class of continuous and nondecreasing ... U and by using (3.5) and mathematical21comparison of the rate of convergence. The first one was introduced by Berinde [27].He used this idea to compare the rate of convergence of Picard and ... {xn}∞n=1converges to a fixed point of T.We now obtain the convergence theorem of W(T,N )-iteration. The proof is omittedbecause it is similar as above theorem and Theorem 2.2 of [4].Theorem 2.2 Let E be...
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