Báo cáo toán học: "On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices" pps
Báo cáo toán học: " On externally complete subsets and common fixed points in partially ordered sets" potx
... amazingthat these ideas extend nicely to the case of partially ordered sets. The ideas in Abu-Sbeih and Khamsi Fixed Point Theory and Applications 2011, 2011:97http://www.fixedpointtheoryandapplications.com/content/2011/1/97Page ... X.Define the lower and upper cones byCl(M)= {x ∈ X; there exists m ∈ M such that x ≺ m}Abu-Sbeih and Khamsi Fixed Point Theory and Applications 2011, 2011:97http://www.fixedpointtheoryandapplications.com/content/2011/1/97Page ... if and only if Mis convex, Dedekind complete, and any chain C ⊂ M has a least upper bound in M.Abu-Sbeih and Khamsi Fixed Point Theory and Applications 2011, 2011:97http://www.fixedpointtheoryandapplications.com/content/2011/1/97Page...
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Báo cáo toán học: "On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs" ppt
... ( G ) of the graph G is definedas the sum of singular values of the incidence matrix [9]. The directed incidence energyDIE(G) is defined as the sum of singular values of the directed incidence ... LEL(G) in [10]. The connection between IE and Laplacianeigenvalues (for bipartite graphs) was first pointed out in [6]. For more information on IE and DIE/LEL, see [7, 14] and the references therein. In ... always positive in a neighbor of the origin. We determine t he Q-sp ectrum and the L-spectrum of H2n. If e is the edge joining two copies of Kn, then G − e is 2Kn. So, the Q-spectrum of...
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Báo cáo toán học: "Parking functions, empirical processes, and the width of rooted labeled trees" pps
... easily to binary trees : the BFS randomwalk for a binary tree is a ruin sequence, and in the correspondence between ruin sequences and general trees, the maximum of the ruin sequence is within O(1) ... at each of the n following stages of the BFS, the vertex x at the head of the queue is removed from the queue, and all “new” neighbors of x areaddedattheendof the queue, in increasing order. ... drawnat random in the subset Ωnof labeled trees rooted at 0. The BFS of the rooted labeledtree starts with the root, 0, and is implemented by maintaining a queue Q, that is initially(0). Then,...
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Báo cáo toán học: "On edge colorings with at least q colors in every subset of p vertices" ppsx
... multicolorings.Among many other interesting results and problems in [3] Erd˝os and Gy´arf´as deter-mined for every p the smallest q (qlin=p2− p + 3) for which f (n, p, q) is linear in n and ... to the case when p and q are fixed and n tends to in nity. The studyof f(n, p, q) leads to many interesting and difficult problems. For example determiningf(n, p, 2) is equivalent to determining ... quadratic in n. They raised the question whether perhaps this is the only q value which results in a linear f (n, p, q). In this paper we study the behavior of f(n, p, q) between the linear and quadratic...
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Báo cáo toán học: "Weighted Aztec Diamond Graphs and the Weyl Character Formula" doc
... with integers. Given a matching m of the Aztec diamond graph A, define the weight of the matching (m) to be the productof the weights of all the edges in the matching. Then the weight of the ... to the Aztec diamond of ordern in which the vertices are the squares and an edge joins two vertices if and only if the corresponding squares are adjacent in the Aztec diamond. A perfect matching ... by the perfect matchings of the Aztec diamondgraph. The matchings of other graphs (such as the ones associated to fortresses and dungeons in [Y], [C2], and [P2]) may have similar interesting...
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Báo cáo toán học: "Chromatic Graphs, Ramsey Numbers and the Flexible Atom Conjecture" potx
... concave down. By finding the zeros of this polynomial in termsof n and then maximizing (over n) the greatest of them, we can find the c which willguarantee the inequality in (6). For n ≥ 2, it ... Bm+for m ≤ . Then by making superficial changes to the remainder of the proof we establish the result for the nonsymmetric case. Thus we have the following: the electronic journal of combinatorics ... (iii), as does the coloring of K8which shows R(4, 3) ≥ 9, the colorings of K16that show R(3, 3, 3) ≥ 17,both “twisted” and “untwisted”, and the coloring of K29given in [7] and [4] that showsthat...
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Báo cáo toán học: "Compression of root systems and the E-sequence" pptx
... isomorphism, the roots decorating the vertices will have changed. Furthermore, the construction of˜Drespects the fact that the edges in the Dynkin diagram represent the inner products of the the electronic ... non-orthogonal if there is some i such thatcrossing out the ithrow and the ithcolumn succeeds in crossing out both α and β. Figure 1shows the roots orthogonal to x3− x5 in A5. In type E, ... yj and yj.If {i, i} ∩ {j, j} = ∅ then (x|y) = 0 and x and y agree in exactly one coordinate. If#({i, i} ∩ {j, j}) = 1 then (x|y) = 0 and x and y agree in two or three coordinates....
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Báo cáo toán học: " On cubic planar hypohamiltonian and hypotraceable graph" pptx
... cycle, such that there are fii-gons in the exteriorof the Hamiltonian cycle and f′ii-gons in the interior of the Hamiltonian cycle. Theni(i − 2)(fi− f′i) = 0. (1) The theorem can be ... additional edges incident to x′ and y′. By Theorem 2.3 and Propo sition 3.3 there is a cycle of length 4692 in the remaininggraph, which proves the coro llar y. ✷ The following definition is due to ... every integer m ≥ 0 in 1981. However, the question whether thereexist smaller cubic hypohamiltonian graphs and whether there exists a po sitive integer N ,such that for every integ er n ≥ N there...
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Báo cáo toán học: "On variants of Conway and Conolly’s Meta-Fibonacci recursions" potx
... interpretationof the corresponding recursion under sets of initial conditions that are forced on by the interpretation itself (see [4] and t he references cited therein). The combinatorial inter-pretation ... = Ek and A(Ek+1+ 1) = A(3) = 2 = Ek+ 1. Assume that the three hypotheseshold up to n, and note since A(i) is slow and unbounded, A−1({En}) = [α, β]. In the following, if k = 1 then take ... 1 and c ≥ 1 are integers. Under what set of para meters k, a, b, c and initial conditions is the resulting sequence A(n) defined for all positive integers and/ orslow-growing?AcknowledgementThe...
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