Báo cáo toán học: "Orthogonal art galleries with holes: a coloring proof of

Báo cáo toán học: "Orthogonal art galleries with holes: a coloring proof of Aggarwal’s Theorem" potx

... resultant quadrilateralization graph. Let us recall that a quadrilateralization of an orthogonal polygon P (with or without holes) is a partitioning of P into a set of convex quadrilaterals with pairwise ... Orthogonal galleries with one holeLet Q be a quadrilateralization of an n-vertex orthogonal polygon P with one hole. Byadding both diagonals to each quadrilateral of Q,wegetthequadrilateralization ... quadrilateralization graph, and it is similar to that of Kahn and others for orthogonal polygons without holes. Consequently, we providean alternate proof of Aggarwal’s theorem asserting that...

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Báo cáo toán học: "Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theorem" potx

... journal of combinatorics 11 (2004), #R62 3Random Cayley graphs are expanders: a simple proof of the Alon–Roichman theoremZEPH LANDAUDepartment of MathematicsCity College of New Yorklandau@sci.ccny.cuny.edu A LEXANDER ... adjacency matrix of the graph is less than ε as long as k ≥ (cε+ o(1)) log |G|. Their proof involves a clever combinatorial argument that controls the behavior of random walks takenon ... result above with a smaller constant cε.1 Introduction A beautiful theorem of N. Alon and Y. Roichman [4] asserts that random Cayley graphs areexpanders. Speciﬁcally, they study the spectrum of...

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Báo cáo toán học: "Periodicity and Other Structure in a Colorful Family of Nim-like Arrays" pdf

... described each of the arrays A sasendowing N0 with the algebraic structure of a quasigroup [22]. We discuss resultsrelated to this algebraic approach in [1]; that article deals with the same family ... operation of Nim-addition. In particular, these arrays display periodic behavior along rows anddiagonals. We explain how various features of computer-generated graphicsdepicting these arrays are ... 2010Mathematics Subject Classiﬁcation: 68R15, 9 1A4 6AbstractWe study aspects of the combinatorial and graphical structure shared by a certain family of recursively generated arrays related to...

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Báo cáo toán học: "Orthogonal arrays with parameters OA(s3, s2+s+1, s, 2) and 3-dimensional projective geometries" pot

... from a set S that contains s symbols is said to be anorthogonal array with s levels, strength t and index λ if every N ×t subarray of A contains∗Osaka prefectual Nagano high school, 1-1-2 Hara, ... Hara, Kawachinagano, Osaka, Japan,e-mail; denen482@yahoo.co .jpthe electronic journal of combinatorics 18 (2011), #P69 1 PROOF. From Lemmas A, B, C and the theorem of Veblen and Young, we have ... case.the electronic journal of combinatorics 18 (2011), #P69 8each t−tuple based on S exactly λ times as a row. We denote the array A by OA(N, k, s, t).Orthogonal arrays with parameters OA(sn,...