Báo cáo toán học: "The Cube Recurrence" docx

Báo cáo toán học: "The approximative point spectrum of a subnormal operator " docx

... class="bi x0 y1 w1 h 2" alt ="" ...

Báo cáo toán học: " THE THREE DIMENSIONAL POLYOMINOES OF MINIMAL AREA" docx

... polyominoes. The area |c| of the polyomino c is the number of its unit squares. We denote by Cn the set of all the polyominoes of area n. The perimeter P (c) of a polyomino c is the number of ... c1and c2. Putting these facts together, wesee that for the values of n listed in the theorem, the sets of the minimal antecedentsthrough the sequence of transformations of the canonical polyomino ... 2 is minimal. It cannotbe grown through the minimal polyominoes. 12Theorem 2.6. The set of minimal polyominoes Mncoincides with the set of principal polyominoes Mnif and only if the integer...

Báo cáo toán học: "The Rectilinear Crossing Number of K10 is 62" docx

... point is a vertex. Such a drawing is said to be a rectilinear drawing of G.Therectilinear crossing number of G,denotedν(G), is the fewest number of edge crossings attainable over all rectilinear ... rectilinear drawing of Kn is a triangle. Prove that the convex hull of any optimal rectilinear drawing of Kn is a triangle.2. Given a rectilinear drawing of G,theplanar subdivision of G is the graphobtained ... 60.Proof: By way of contradiction, assume that there exists a rectilinear drawing of K10with 60 crossings. Since each edge crossing comprises of four vertices, the sum of responsibilities of each...

Báo cáo toán học: "The umbral transfer-matrix method IV. Counting self-avoiding polygons and walks" docx

... The Umbral Transfer-Matrix Method. IV. Counting Self-Avoiding Polygons and Walks, this article.[Z5] Doron Zeilberger, The Umbral Transfer-Matrix Method. V. The Goulden-Jackson Cluster Method ... F2(q).the electronic journal of combinatorics 8 (2001), #R28 16 The umbral transfer-matrix method IV. Counting self-avoiding polygons and walksDoron ZEILBERGER1<zeilberg@math.temple.edu>Submitted: ... Zeilberger, The Umbral Transfer-Matrix Method. I. Foundations,J.Comb.TheorySer.A91 (2000), 451-463. [Rota memorial issue].[Z2] Doron Zeilberger, The Umbral Transfer-Matrix Method. II. Counting PlanePartitions,...

Báo cáo toán học: "The hexad game" docx

... are thereforehexads. Moreover, it is impossible to move from one hexad to another in the game(because a pair of hexads contain at most four common points). Hence to show thatthe hexads are the ... on hexads, we can choose co-ordinates so that any given hexad forms the left pair of columns (the left brick) of the Minimog. Moreover, the M12-stabilizer of a hexad is transitive on the hexad, ... of M12.3. The P -positions of the hexad game.We now give our new, non-enumerative proof of:Theorem. The P-positions of the hexad game are the (special) hexads of the shuﬄenumbered Steiner...

Báo cáo toán học: "The cube polynomial and its derivatives: the case of median graphs" pps

... . the electronic journal of combinatorics 10 (2003), #R3 5 Proof. The proof is by induction on the number of vertices of a graph. The n -cube Qn,n ≥ 1, can be obtained as the expansion of the ... graphs Ue and derivec(s+1)(G, −1) =e∈F(G)θs(Ue)=θs+1(G). the electronic journal of combinatorics 10 (2003), #R3 8 The cube polynomial and its derivatives: the case of median graphsBoˇstjan ... properties, is up to the factor f(Q0,x) the cube polynomial. The derivation ∂G of a median graph G isintroduced and it is proved that the cube polynomial is the only function f with the property f(G,...

Báo cáo toán học: "The Cube Recurrence" docx

... be worth mentioning that the cube recurrence can be written in a slightlymore symmetrical fashion than above: the families of functions (fi,j,k) satisfying the cube recurrence can be made to ... 2004Keywords: cube recurrence, grove, Gale-Robinson sequenceMR Subject Classiﬁcations: 05A15, 05E99, 11B83AbstractWe construct a combinatorial model that is described by the cube recurrence,a ... that are in bijection with the terms of these Laurent polynomials, undera generalized form of the cube recurrence; Propp’s observations, among other interestingresults, will then follow directly.Aside...

Báo cáo toán học: "The cover pebbling theorem Jonas Sj¨strand o" docx

... that admits no cover pebbling, allpebbles may be concentrated to one of the fat nodes1with cover pebbling still not possible.Proof. Start with a distribution that admits no cover pebbling. If ... cover pebbling fromf exceeds the total value of the pebbles. Therefore, cover pebbling is not possible withall pebbles initially on f . 4 The cover number for some classes of graphsThe cover ... thecost of cover pebbling from v.In the graph below, 8 + 8 + 4 + 2 + 1 pebbles on v are necessary and suﬃcient for a cover pebbling if w is the 1-distribution.vFigure 1: A cover pebbling from...

Báo cáo toán học: "The combinatorics of orbital varieties closures of nilpotent order 2 in sl n" docx

... electronic journal of combinatorics 12 (20 05) #R21 20 The combinatorics of orbital varieties closures of nilpotent order 2 in sl nAnna Melnikov*Department of Mathematics,University of Haifa,31905 ... element of nilpotent order 2 or in other words X 2 =0. Thus, we get a completecombinatorial description of inclusion of orbital varieties closures of nilpotent order 2 in sl n.1. 12 The body of ... Young tableaux with 2 columns or with 2 rows. This fact has very interesting geometric implications for orbital varieties of nilpotent order 2 in special linear algebra sl n.1. Introduction1.1...

Báo cáo toán học: "The non-crossing graph" docx

... − Θ(1)) ≤ χ(NCn) ≤ n(log2n−1).1 IntroductionTwo sets are non-crossing if they are disjoint or one contains another. The non-crossing graph NCnis the graph whose vertex set is the set ... Published: Jan 25, 2006Mathematics Subject Classiﬁcations: 05C88, 05C89AbstractTwo sets are non-crossing if they are disjoint or one contains the other. The non-crossing graph NCnis the ... graph whose vertex set is the set of nonempty subsets of[n]={1, ,n} with an edge between any two non-crossing sets.Various facts, some new and some already known, concerning the chromaticnumber,...

Báo cáo toán học: "The Linear Complexity of a Graph" docx

... recoverable using any algorithm designed to computethe product of an adjacency matrix of the graph and an arbitrary vector. The linear complexity of a graph may therefore be seen as a measure of ... adjacency matrices of graphs, and a working knowledge of the linear complexity of a linear transformation. An excellent reference for linear complexity, and algebraic complexity in general, is [4]. ... required to multiply that matrix and anarbitrary vector. In this paper, we deﬁne the linear complexity of a graph to be the linear complexity of any one of its associated adjacency matrices. We then...

Báo cáo toán học: "The Strongly Regular (45, 12, 3, 3) Graphs" docx

... 7(1),(2000).[12] E. Spence, Strongly Regular Graphs,URL:http://www.maths.gla.ac.uk/~es/srgraphs.html, (2004).the electronic journal of combina torics 13 (2006), #R32 9 (v, k, ,à) =(45, 12, 3, 3), providing ... at least n − 25.the electronic journal of combina torics 13 (2006), #R32 3 The Strongly Regular (45, 12, 3, 3) GraphsKris Coolsaet, Jan DegraerDepartment of Applied Mathematics and Computer ... size for each srg(45, 12, 3, 3). 5 ResultsAs stated in the introduction, both computer programs independently proved that thereare up to isomorphism exactly 78 diﬀerent strongly regular graphs...

Báo cáo toán học: "The maximum number of perfect matchings in graphs with a given degree sequence" docx

... square all-1 matrix.Proof of Theorem 1.1: The square of the number of perfect matchings of G countsordered pairs of such matchings. We claim that this is the number of spanning 2-regularsubgraphs ... Cuckler and J. Kahn, Entropy bounds for perfect matchings and Hamiltoniancycles, to appear.[3] S. Friedland, An upper bound for the number of perfect matchings in graphs, arXiv:0803.0864v1, 6 March ... rows andcolumns of the adjacency matrix of G it is a block diagonal matrix in which every blockis an all-1 square matrix, and as our graph G has no loops, this means that it is a union of complete...

Báo cáo toán học: "The universal embedding of the near polygon Gn" docx

... Bardoe. On the universal embedding of the near- hexagon for U4(3). Geom.Dedicata 56 (1995), 7–17.[2] A. Blokhuis and A. E. Brouwer. The universal embedding dimension of the near polygon on the 1-factors ... deter-mine the absolutely universal embedding of this near polygon. We show that the generating and embedding ranks of Gnare equal to2nn. We also show that the absolutely universal embedding of ... line L, there exists a unique point on L nearest to p. Here,distances are measured in the point or collinearity graph Γ of S. If d is the diameter of Γ, then the near polygon is called a near 2d-gon....

Báo cáo toán học: "The spectral excess theorem for distance-regular graphs: a global (over)view" docx

... distance-regular if each vertex has at least one vertex at distance d and its distance-dadjacency matrix A dis a polynomial of degree d in the adjacency matrix A. This result ishalfway towards the spectral ... distance-regular. Thisconclusion is the spectral excess theorem for this case.the electronic journal of combinatorics 15 (2008), #R129 4 The spectral excess theorem for distance-regular graphs: a global ... 2008Mathematics Subject Classiﬁcation: 05E30, 05B20Keywords: distance-regular graphs, eigenvalues of graphs, spectral excess theorem AbstractDistance-regularity of a graph is in general not...

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