Titlebook: Combinatorics and Finite Geometry; Steven T. Dougherty Textbook 2020 The Editor(s) (if applicable) and The Author(s), under exclusive lice

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https://doi.org/10.1007/978-981-16-6879-1This chapter describes a series of combinatorial objects including Hadamard matrices, Latin hypercubes, association schemes, and partially ordered sets. The algebraic and combinatorial properties of these objects are discussed.

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airborne

Sèmévo Ida Tognisse,Jules DegilaThis chapter introduces a version of the well-known Tic-Tac-Toe game which can be played on designs and finite geometries. This game helps develop students’ geometric intuition. The theory of combinatorial games is applied to determine when the first player has a winning strategy and when the second player can force a draw.

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https://doi.org/10.1007/978-981-19-2764-5Early in the text we encountered the following diagram.

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Affine and Projective Planes,This chapter gives fundamental results on finite affine and projective planes. It provides detailed proofs on various counting results concerning these planes such as the number of points, lines, points on a line, and lines through a point. It describes the canonical relation between affine planes and mutually orthogonal Latin squares.

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Infelicity

Higher Dimensional Finite Geometry,This chapter gives a basic introduction of linear algebra and uses this setting to describe higher dimensional affine and projective geometries. It includes proofs of the Bruck–Ryser theorem and Desargues’ theorem. It further describes Baer subplanes, arcs, and ovals. It concludes with a description of certain non-Desarguesian planes.