Báo cáo toán học: "The Cube Recurrence" docx

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Ngày tải lên: 05/08/2014, 10:20

... polyominoes. The area |c| of the polyomino c is the number of its unit squares. We denote by C n the set of all the polyominoes of area n. The perimeter P (c) of a polyomino c is the number of ... c 1 and c 2 . Putting these facts together, we see that for the values of n listed in the theorem, the sets of the minimal antecedents through the sequen...

Ngày tải lên: 07/08/2014, 06:20

... point is a vertex. Such a drawing is said to be a rectilinear drawing of G.Therectilinear crossing number of G,denoted ν(G), is the fewest number of edge crossings attainable over all rectilinear ... rectilinear drawing of K n is a triangle. Prove that the convex hull of any optimal rectilinear drawing of K n is a triangle. 2. Given a rectilinear drawing...

Ngày tải lên: 07/08/2014, 06:22

... 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 ... F 2 (q). the electronic journal of combinatorics 8 (2001), #R28 16 The umbral transfer-matrix method IV. Counting self-avoiding polygons and walks Doron ZEILBER...

Ngày tải lên: 07/08/2014, 06:22

... are therefore hexads. 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 that the 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 M 12 - stabilizer of a hexad is transitive on the...

Ngày tải lên: 07/08/2014, 06:23

... . 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 Q n , n ≥ 1, can be obtained as the expansion of the ... graphs U e and derive c (s+1) (G, −1) =  e∈F(G) θ s (U e )=θ s+1 (G). the electronic journal of combinatorics 10 (2003), #R3 8 The cube polynomial and its...

Ngày tải lên: 07/08/2014, 07:21

... be worth mentioning that the cube recurrence can be written in a slightly more symmetrical fashion than above: the families of functions (f i,j,k ) satisfying the cube recurrence can be made to ... 2004 Keywords: cube recurrence, grove, Gale-Robinson sequence MR Subject Classifications: 05A15, 05E99, 11B83 Abstract We construct a combinatorial model that is described by the cube recurr...

Ngày tải lên: 07/08/2014, 08:22

... that admits no cover pebbling, all pebbles may be concentrated to one of the fat nodes 1 with cover pebbling still not possible. Proof. Start with a distribution that admits no cover pebbling. If ... cover pebbling from f exceeds the total value of the pebbles. Therefore, cover pebbling is not possible with all pebbles initially on f .  4 The cover number for some classe...

Ngày tải lên: 07/08/2014, 08:22

... electronic journal of combinatorics 12 (20 05) #R21 20 The combinatorics of orbital varieties closures of nilpotent order 2 in sl n Anna Melnikov* Department of Mathematics, University of Haifa, 31905 ... element of nilpotent order 2 or in other words X 2 =0. Thus, we get a complete combinatorial description of inclusion of orbital varietie...

Ngày tải lên: 07/08/2014, 08:22

... − Θ(1)) ≤ χ(NC n ) ≤ n(log 2 n−1). 1 Introduction Two sets are non-crossing if they are disjoint or one contains another. The non-crossing graph NC n is the graph whose vertex set is the set ... Published: Jan 25, 2006 Mathematics Subject Classifications: 05C88, 05C89 Abstract Two sets are non-crossing if they are disjoint or one contains the other. The non- crossing graph NC n is the...

Ngày tải lên: 07/08/2014, 13:21

... recoverable using any algorithm designed to compute the 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 al...

Ngày tải lên: 07/08/2014, 13:21

... 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) Graphs Kris Coolsaet, Jan Degraer Departm...

Ngày tải lên: 07/08/2014, 13:21

... square all-1 matrix. Proof of Theorem 1.1: The square of the number of perfect matchings of G counts ordered pairs of such matchings. We claim that this is the number of spanning 2-regular subgraphs ... Cuckler and J. Kahn, Entropy bounds for perfect matchings and Hamiltonian cycles, to appear. [3] S. Friedland, An upper bound for the number of perfect matching...

Ngày tải lên: 07/08/2014, 15:22

... Bardoe. On the universal embedding of the near- hexagon for U 4 (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 G n are equal to  2...

Ngày tải lên: 07/08/2014, 15:22

... distance-regular if each vertex has at least one vertex at distance d and its distance-d adjacency matrix A d is a polynomial of degree d in the adjacency matrix A. This result is halfway towards the spectral ... distance-regular. This conclusion is the spectral excess theorem for this case. the electronic journal of combinatorics 15 (2008), #R129 4 The spectral excess...

Ngày tải lên: 07/08/2014, 21:20