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Located at the southwest corner of Lake Turkana in northern Kenya, Lothagam represents one of the most important intervals in African prehistory. Early human remains are restricted in distribution to Africa and the acquisition of an upright bipedal striding gait, the hallmark of humanity, appears to be at least circumstantially linked to the reduction of equatorial forests and the spread of grasslands on that continent. The diverse Lothagam fauna documents the end-Miocene transition from forested to more open habitats that were exploited by grazing horses and antelopes, hippos, giant pigs, and true elephants. It also includes spectacularly complete fossil carnivore skeletons and some of the oldest human remains.Enlisting a team of highly qualified specialists, this book provides the geologic context and dating framework for the Lothagam fossiliferous sequences, describes the immense diversity of vertebrate fossils recovered from the Late Miocene and Early Pliocene sediments, and synthesizes the results to interpret the changing paleoenvironments that prevailed at this site. The book will interest anthropologists, paleontologists, geologists, and anyone interested in human origins.

Vertebrates, Fossil --- Paleontology --- Animals, Fossil --- Vertébrés fossiles --- Paléontologie --- Animaux fossiles --- Lothagam Site (Kenya) --- Lothagam (Kenya : Site archéologique) --- Lothagam Site (Kenya). --- Vertébrés fossiles --- Paléontologie --- Lothagam (Kenya : Site archéologique) --- Animal fossils --- Animals, Antediluvian --- Animals, Prehistoric --- Antediluvian animals --- Fauna, Prehistoric --- Prehistoric animals --- Prehistoric fauna --- Miocene Epoch --- Fossils --- Chordata, Fossil --- Kenya --- Antiquities --- Vertebrates [Fossil ] --- Miocene --- Animals [Fossil ]

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This book covers a wide variety of topics in combinatorics and graph theory. It includes results and problems that cross subdisciplines, emphasizing relationships between different areas of mathematics. In addition, recent results appear in the text, illustrating the fact that mathematics is a living discipline. The second edition includes many new topics and features: • New sections in graph theory on distance, Eulerian trails, and Hamiltonian paths. • New material on partitions, multinomial coefficients, and the pigeonhole principle. • Expanded coverage of Pólya Theory to include de Bruijn’s method for counting arrangements when a second symmetry group acts on the set of allowed colors. • Topics in combinatorial geometry, including Erdos and Szekeres’ development of Ramsey Theory in a problem about convex polygons determined by sets of points. • Expanded coverage of stable marriage problems, and new sections on marriage problems for infinite sets, both countable and uncountable. • Numerous new exercises throughout the book. About the First Edition: ". . . this is what a textbook should be! The book is comprehensive without being overwhelming, the proofs are elegant, clear and short, and the examples are well picked." — Ioana Mihaila, MAA Reviews.

Análisis combinatorio --- Grafos, Teoría de --- Discrete mathematics --- Combinatorial analysis --- Graph theory --- Combinatorial analysis. --- Graph theory. --- Discrete mathematics. --- Combinatorics. --- Mathematical logic. --- Discrete Mathematics. --- Mathematical Logic and Foundations. --- Combinatorics --- Algebra --- Mathematical analysis --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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