{"title":"Combinatorics","description":"\u003cp\u003eCombinatorics is a branch of mathematics centered on counting, arrangement, and optimization of discrete structures. This subject investigates finite sets, permutations, combinations, graph theory, and related problems, offering essential foundations for statistics, computer science, and logic. Readers explore how principles of selection and arrangement impact everything from algorithms to coding theory.\u003c\/p\u003e\u003cp\u003eTo deepen your mathematical research, use combinatorics to supplement study in algebra, probability, or mathematical logic, or focus on a particular theme within discrete mathematics such as enumeration, partitions, or graph connectivity. 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The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543615930658,"sku":"9789814733441-new","price":61.48,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814733441.jpg?v=1776386653"},{"product_id":"crystal-bases-representations-combinatorics-9789814733434-new","title":"Crystal Bases: Representations and Combinatorics","description":"\u003cp\u003eThis unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. 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The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.\u003c\/p\u003e\u003cp\u003eThe selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity.\u003c\/p\u003e\u003cp\u003eAs the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.\u003c\/p\u003e\u003cp\u003eThe Solution Manual is available upon request for all instructors who adopt this book as a course text.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543675437346,"sku":"9789814460002-new","price":61.5,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814460002.jpg?v=1776389164"},{"product_id":"walk-through-combinatorics-3ed-9789814335232-new","title":"Walk Through Combinatorics (3ed)","description":"\u003cp\u003eThis is a textbook for an introductory combinatorics course lasting one or two semesters. 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Randomized algorithms, which are now ubiquitous because of their applications to cryptography; and Online algorithms, which are essential in fields as diverse as operating systems (caching, in particular) and stock-market predictions.This self-contained book is intended for undergraduate students in computer science and mathematics.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543818797346,"sku":"9789814271400-new","price":47.97,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814271400.jpg?v=1776392424"},{"product_id":"principles-techniques-combinatorics-solutions-manual-9789813238848-new","title":"Principles and Techniques in Combinatorics: Solutions Manual","description":"\u003cp\u003eThe solutions to each problem are written from a first principles approach, which would further augment the understanding of the important and recurring concepts in each chapter. 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Extra examples were added to some sections where readers asked for them.\u003c\/p\u003e\u003cp\u003eThe selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.\u003c\/p\u003e\u003cp\u003eThe book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.\u003c\/p\u003e\u003cp\u003eThe Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to sales@wspc.com.\u003c\/p\u003e\u003cp\u003eThe previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. 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While succinct, this edition is mathematically rigorous, covering the foundations for both computer scientists and mathematicians with interest in the algorithmic foundations of Computer Science.\u003c\/p\u003e\u003cp\u003eBesides expositions on traditional algorithms such as Greedy, Dynamic Programming and Divide \u0026amp; Conquer, the book explores two classes of algorithms that are often overlooked in introductory textbooks: Randomised and Online algorithms -- with emphasis placed on the algorithm itself. 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