| Document Type
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BL
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| Record Number
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948893
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| Doc. No
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b703263
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| Main Entry
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Brualdi, Richard A.
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| Title & Author
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Introductory combinatorics /\ Richard A. Brualdi.
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| Edition Statement
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5th ed.
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| Publication Statement
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Upper Saddle River, N.J. :: Pearson/Prentice Hall,, ©2010.
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| Page. NO
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xii, 605 pages :: illustrations ;; 24 cm
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| ISBN
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0136020402
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: 9780136020400
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| Bibliographies/Indexes
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Includes bibliographical references (pages 596-597) and index.
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| Contents
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9: Systems Of Distinct Representatives -- 9-1: General problem formulation -- 9-2: Existence of SDRs -- 9-3: Stable marriages -- 9-4: Exercises -- 10: Combinatorial Designs -- 10-1: Modular arithmetic -- 10-2: Block designs -- 10-3: Steiner triple systems -- 10-4: Latin squares -- 10-5: Exercises -- 11: Introduction To Graph Theory -- 11-1: Basic properties -- 11-2: Eulerian Trails -- 11-3: Hamilton paths and cycles -- 11-4: Bipartite multigraphs -- 11-5: Trees -- 11-6: Shannon switching game -- 11-7: More on trees -- 11-8: Exercises -- 12: More On Graph Theory -- 12-1: Chromatic number -- 12-2: Plane and planar graphs -- 12-3: Five-color theorem -- 12-4: Independence number and clique number -- 12-5: Matching number -- 12-6: Connectivity -- 12-7: Exercises -- 13: Digraphs And Networks -- 13-1: Digraphs -- 13-2: Networks -- 13-3: Matchings in bipartite graphs revisited -- 13-4: Exercises -- 14: Polya Counting -- 14-1: Permutation and symmetry groups -- 14-2: Burnside's theorem -- 14-3: Polya's counting formula -- 14-4: Exercises -- Answers and hints to exercises -- Bibliography -- Index.
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Preface -- 1: What Is Combinatorics? -- 1-1: Example: Perfect covers of chessboards -- 1-2: Example: Magic squares -- 1-3: Example: Four-color problem -- 1-4: Example: Problem of the 36 officers -- 1-5: Example: Shortest-route problem -- 1-6: Example: Mutually overlapping circles -- 1-7: Example: Game of Nim -- 1-8: Exercises -- 2: Permutations And Combinations -- 2-1: Four basic counting principles -- 2-2: Permutations of sets -- 2-3: Combinations (subsets) of sets -- 2-4: Permutations of multisets -- 2-5: Combinations of multisets -- 2-6: Finite probability -- 2-7: Exercises -- 3: Pigeonhole Principle -- 3-1: Pigeonhole principle: Simple form -- 3-2: Pigeonhole principle: Strong form -- 3-3: Theorem of Ramsey -- 3-4: Exercises -- 4: Generating Permutations And Combinations -- 4-1: Generating permutations -- 4-2: Inversions in permutations -- 4-3: Generating combinations -- 4-4: Generating r-subsets -- 4-5: Partial orders and equivalence relations -- 4-6: Exercises -- 5: Binomial Coefficients -- 5-1: Pascal's Triangle -- 5-2: Binomial theorem -- 5-3: Unimodality of binomial coefficients -- 5-4: Multinomial theorem -- 5-5: Newton's binomial theorem -- 5-6: More on partially ordered sets -- 5-7: Exercises -- 6: Inclusion-Exclusion Principle And Applications -- 6-1: Inclusion-exclusion principle -- 6-2: Combinations with repetition -- 6-3: Derangements -- 6-4: Permutations with forbidden positions -- 6-5: Another forbidden position problem -- 6-6: Mobius inversion -- 6-7: Exercises -- 7: Recurrence Relations And Generating Functions -- 7-1: Some number sequences -- 7-2: Generating functions -- 7-3: Exponential generating functions -- 7-4: Solving linear homogeneous recurrence relations -- 7-5: Nonhomogeneous recurrence relations -- 7-6: Geometry example -- 7-7: Exercises -- 8: Special Counting Sequences -- 8-1: Catalan numbers -- 8-2: Difference sequences and stirling numbers -- 8-3: Partition numbers -- 8-4: Geometric problem -- 8-5: Lattice paths and Schroder numbers -- 8-6: Exercises.
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| Abstract
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From the Publisher: This trusted best-seller emphasizes combinatorial ideas-including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatorial structures (matchings, designs, graphs), and flows in networks. The Fifth Edition clarifies the exposition throughout and adds a wealth of new exercises.
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| Subject
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Combinatorial analysis, Textbooks.
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| Subject
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Computer science-- Mathematics.
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| Subject
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Combinatorial analysis.
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| Subject
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Computer science-- Mathematics.
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| Dewey Classification
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511/.6
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| LC Classification
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QA164.B76 2010
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