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Combinatorial analysis.

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The volume LNCS 12296 constitutes the papers of the 17th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research which will be held online in September 2020. The 32 regular papers presented together with 4 abstracts of fast-track papers were carefully reviewed and selected from a total of 72 submissions. Additionally, this volume includes the 4 abstracts and 2 invited papers by plenary speakers. The conference program also included a Master Class on the topic “Recent Advances in Optimization Paradigms and Solving Technology".

Numerical analysis. --- Numeric Computing. --- Mathematical analysis --- Combinatorial optimization --- Artificial intelligence --- Constraint programming (Computer science) --- Data processing --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization --- Numerical Analysis.

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Analyse combinatoire. --- Ramsey, Théorie de. --- Ramsey theory --- Combinatorial analysis --- Ramsey numbers.

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"The so-called "pinched disk" model of the Mandelbrot set is due to A. Douady, J. H. Hubbard and W. P. Thurston. It can be described in the language of geodesic laminations. The combinatorial model is the quotient space of the unit disk under an equivalence relation that, loosely speaking, "pinches" the disk in the plane (whence the name of the model). The significance of the model lies in particular in the fact that this quotient is planar and therefore can be easily visualized. The conjecture that the Mandelbrot set is actually homeomorphic to this model is equivalent to the celebrated MLC conjecture stating that the Mandelbrot set is locally connected. For parameter spaces of higher degree polynomials no combinatorial model is known. One possible reason may be that the higher degree analog of the MLC conjecture is known to be false. We investigate to which extent a geodesic lamination is determined by the location of its critical sets and when different choices of critical sets lead to essentially the same lamination. This yields models of various parameter spaces of laminations similar to the "pinched disk" model of the Mandelbrot set"--

Geodesics (Mathematics) --- Polynomials. --- Invariant manifolds. --- Combinatorial analysis. --- Dynamics. --- Géodésiques (mathématiques) --- Polynômes. --- Variétés invariantes. --- Analyse combinatoire. --- Dynamique.

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This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.

Combinatorial analysis. --- Finite geometries. --- Geometries, Finite --- Combinatorial geometry --- Combinatorics --- Algebra --- Mathematical analysis --- Discrete mathematics. --- Convex geometry . --- Discrete geometry. --- Discrete Mathematics. --- Convex and Discrete Geometry. --- Discrete mathematics --- Geometry --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis