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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Designs,This chapter introduces the topic of finite combinatorial designs. The defining parameters of the designs are determined and their restrictions are proved. Special attention is given to Steiner triple systems, nets, and biplanes.

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Combinatorial Objects,This 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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,Discrete Probability—A Return to Counting,This chapter gives a brief description of discrete probability. It uses the combinatorial counting properties developed earlier in the text to compute various probabilities.

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Cryptology,This chapter introduces the fundamentals of cryptology. It describes the basic combinatorial principles involved in substitution ciphers and the German Enigma machine. It then develops the main public-key encryption systems including RSA, El Gamal, and the McEliece cryptographic system based on error-correcting codes.

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Games and Designs,This 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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Manish Kumar Singh,Kamlesh Kumar Raghuvanshiic including Fermat’s Little Theorem and Euler’s generalization. It gives foundational results on finite fields to prepare the reader for their use in finite geometry. It concludes with a description of geometric numbers, Catalan numbers, Stirling numbers, and the Towers of Hanoi.

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Sèmévo Ida Tognisse,Jules Degilatructure is a group. It is generally the first structure one encounters in studying abstract algebra. We shall begin with a very elementary study of finite groups, and then we shall study the groups associated with various combinatorial structures.

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Steven T. DoughertyProvides a gentle introduction to combinatorics, finite geometry and related topics.Covers a broad range of related topics including error-connecting codes, cryptology and combinatorial game theory.In