{"product_id":"introduction-to-combinatorics-isbn-9781118637531","title":"Introduction to Combinatorics","description":"\u003cp\u003ePraise for the \u003ci\u003eFirst Edition\u003cbr\u003e \u003cbr\u003e \u003c\/i\u003e “This excellent text should prove a useful accoutrement for any developing mathematics program . . . it’s short, it’s sweet, it’s beautifully written.” —\u003ci\u003eThe Mathematical Intelligencer\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e“Erickson has prepared an exemplary work . . . strongly recommended for inclusion in undergraduate-level library collections.” —\u003ci\u003eChoice\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eFeaturing a modern approach, \u003ci\u003eIntroduction to Combinatorics, Second Edition\u003c\/i\u003e illustrates the applicability of combinatorial methods and discusses topics that are not typically addressed in literature, such as Alcuin’s sequence, Rook paths, and Leech’s lattice. The book also presents fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise questions and observations.\u003c\/p\u003e \u003cp\u003eMany important combinatorial methods are revisited and repeated several times throughout the book in exercises, examples, theorems, and proofs alike, allowing readers to build confidence and reinforce their understanding of complex material. In addition, the author successfully guides readers step-by-step through three major achievements of combinatorics: Van der Waerden’s theorem on arithmetic progressions, Pólya’s graph enumeration formula, and Leech’s 24-dimensional lattice.  Along with updated tables and references that reflect recent advances in various areas, such as error-correcting codes and combinatorial designs, the \u003ci\u003eSecond Edition\u003c\/i\u003e also features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eMany new exercises to help readers understand and apply combinatorial techniques and ideas\u003c\/li\u003e \u003cli\u003eA deeper, investigative study of combinatorics through exercises requiring the use of computer programs\u003c\/li\u003e \u003cli\u003eOver fifty new examples, ranging in level from routine to advanced, that illustrate important combinatorial concepts\u003c\/li\u003e \u003cli\u003eBasic principles and theories in combinatorics as well as new and innovative results in the field\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroduction to Combinatorics, Second Edition\u003c\/i\u003e is an ideal textbook for a one- or two-semester sequence in combinatorics, graph theory, and discrete mathematics at the upper-undergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.\u003c\/p\u003e  \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Basic Counting Methods 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The multiplication principle 1\u003c\/p\u003e \u003cp\u003e1.2 Permutations 4\u003c\/p\u003e \u003cp\u003e1.3 Combinations 6\u003c\/p\u003e \u003cp\u003e1.4 Binomial coefficient identities 10\u003c\/p\u003e \u003cp\u003e1.5 Distributions 19\u003c\/p\u003e \u003cp\u003e1.6 The principle of inclusion and exclusion 23\u003c\/p\u003e \u003cp\u003e1.7 Fibonacci numbers 31\u003c\/p\u003e \u003cp\u003e1.8 Linear recurrence relations 33\u003c\/p\u003e \u003cp\u003e1.9 Special recurrence relations 41\u003c\/p\u003e \u003cp\u003e1.10 Counting and number theory 45\u003c\/p\u003e \u003cp\u003eNotes 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Generating Functions 53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Rational generating functions 53\u003c\/p\u003e \u003cp\u003e2.2 Special generating functions 63\u003c\/p\u003e \u003cp\u003e2.3 Partition numbers 76\u003c\/p\u003e \u003cp\u003e2.4 Labeled and unlabeled sets 80\u003c\/p\u003e \u003cp\u003e2.5 Counting with symmetry 86\u003c\/p\u003e \u003cp\u003e2.6 Cycle indexes 93\u003c\/p\u003e \u003cp\u003e2.7 Pólya’s theorem 96\u003c\/p\u003e \u003cp\u003e2.8 The number of graphs 98\u003c\/p\u003e \u003cp\u003e2.9 Symmetries in domain and range 102\u003c\/p\u003e \u003cp\u003e2.10 Asymmetric graphs 103\u003c\/p\u003e \u003cp\u003eNotes 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 The Pigeonhole Principle 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Simple examples 107\u003c\/p\u003e \u003cp\u003e3.2 Lattice points, the \u003ci\u003eGitterpunktproblem\u003c\/i\u003e, and SET® 110\u003c\/p\u003e \u003cp\u003e3.3 Graphs 115\u003c\/p\u003e \u003cp\u003e3.4 Colorings of the plane 118\u003c\/p\u003e \u003cp\u003e3.5 Sequences and partial orders 119\u003c\/p\u003e \u003cp\u003e3.6 Subsets 124\u003c\/p\u003e \u003cp\u003eNotes 126\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Ramsey Theory 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Ramsey’s theorem 131\u003c\/p\u003e \u003cp\u003e4.2 Generalizations of Ramsey’s theorem 135\u003c\/p\u003e \u003cp\u003e4.3 Ramsey numbers, bounds, and asymptotics 139\u003c\/p\u003e \u003cp\u003e4.4 The probabilistic method 143\u003c\/p\u003e \u003cp\u003e4.5 Sums 145\u003c\/p\u003e \u003cp\u003e4.6 Van der Waerden’s theorem 146\u003c\/p\u003e \u003cp\u003eNotes 150\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Codes 153\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Binary codes 153\u003c\/p\u003e \u003cp\u003e5.2 Perfect codes 156\u003c\/p\u003e \u003cp\u003e5.3 Hamming codes 158\u003c\/p\u003e \u003cp\u003e5.4 The Fano Configuration 162\u003c\/p\u003e \u003cp\u003eNotes 168\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Designs 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 \u003ci\u003et\u003c\/i\u003e-designs 171\u003c\/p\u003e \u003cp\u003eCONTENTS \u003cb\u003eix\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.2 Block designs 175\u003c\/p\u003e \u003cp\u003e6.3 Projective planes 180\u003c\/p\u003e \u003cp\u003e6.4 Latin squares 182\u003c\/p\u003e \u003cp\u003e6.5 MOLS and OODs 185\u003c\/p\u003e \u003cp\u003e6.6 Hadamard matrices 188\u003c\/p\u003e \u003cp\u003e6.7 The Golay code and \u003ci\u003eS\u003c\/i\u003e(5\u003ci\u003e,\u003c\/i\u003e 8\u003ci\u003e,\u003c\/i\u003e 24) 194\u003c\/p\u003e \u003cp\u003e6.8 Lattices and sphere packings 197\u003c\/p\u003e \u003cp\u003e6.9 Leech’s lattice 199\u003c\/p\u003e \u003cp\u003eNotes 201\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Web Resources 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Notation 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eExercise Solutions 211\u003c\/p\u003e \u003cp\u003eReferences 225\u003c\/p\u003e \u003cp\u003eIndex 227\u003c\/p\u003e  \u003cp\u003e“Indeed, Erickson’s Introduction to Combinatoricsis appealing on precisely the count that it is very user-friendly.”  (\u003ci\u003eMAA Reviews\u003c\/i\u003e, 5 January 2014)\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eMARTIN J. ERICKSON, PhD,\u003c\/b\u003e is Professor in the Department of Mathematics at Truman State University. The author of numerous books, including \u003ci\u003eMathematics for the Liberal Arts\u003c\/i\u003e (Wiley), he is a member of the American Mathematical Society, Mathematical Association of America, and American Association of University Professors.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"This excellent text should prove a useful accoutrement for any developing mathematics program . . . it's short, it's sweet, it's beautifully written.\"\u003cbr\u003e —\u003ci\u003eThe Mathematical Intelligencer\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\"Erickson has prepared an exemplary work . . . strongly recommended for inclusion in undergraduate-level library collections.\"\u003cbr\u003e —\u003ci\u003eChoice\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eFeaturing a modern approach, \u003ci\u003eIntroduction to Combinatorics, Second Edition\u003c\/i\u003e illustrates the applicability of combinatorial methods and discusses topics that are not typically addressed in literature, such as Alcuin's sequence, Rook paths, and Leech's lattice. The book also presents fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise questions and observations.\u003c\/p\u003e \u003cp\u003eMany important combinatorial methods are revisited and repeated several times throughout the book in exercises, examples, theorems, and proofs alike, allowing readers to build confidence and reinforce their understanding of complex material. In addition, the author successfully guides readers step-by-step through three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Pólya's graph enumeration formula, and Leech's 24-dimensional lattice.\u003c\/p\u003e \u003cp\u003eAlong with updated tables and references that reflect recent advances in various areas, such as error-correcting codes and combinatorial designs, the \u003ci\u003eSecond Edition\u003c\/i\u003e also features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eMany new exercises to help readers understand and apply combinatorial techniques and ideas\u003c\/li\u003e \u003cli\u003eA deeper, investigative study of combinatorics through exercises requiring the use of computer programs\u003c\/li\u003e \u003cli\u003eOver fifty new examples, ranging in level from routine to advanced, that illustrate important combinatorial concepts\u003c\/li\u003e \u003cli\u003eBasic principles and theories in combinatorics as well as new and innovative results in the field\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroduction to Combinatorics, Second Edition\u003c\/i\u003e is an ideal textbook for a one- or two-semester sequence in combinatorics, graph theory, and discrete mathematics at the upper-undergraduate level. The book is also an excellent reference for anyone interested in the various applications of elementary combinatorics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989457191141,"sku":"NP9781118637531","price":91.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118637531.jpg?v=1761784176","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-combinatorics-isbn-9781118637531","provider":"K12savings","version":"1.0","type":"link"}