Combinatorics

ForewordPreface to the Russian EditionI. General Rules of Combinatorics Superstitious Cyclists Samples with Repetitions Systems of Numeration Combination Lock The Morse Code Signaling at Sea Electronic Computers Genetic Code General Rules of Combinatorics A Domino Problem Crew of a Spaceship A Checkers Problem How Many People Do Not Know a Foreign Language? The Principle of Inclusion and Exclusion Find the Error! The Sieve of ErastothenesII. Samples, Permutations, and Combinations Soccer Tournament Samples without Repetitions Learned Society Permutations A Rook Problem Linguistic Problems Dancing in a Circle Permutations with Repetitions Anagrams Combinations The Genoa Lottery Buying Pastry Combinations with Repetitions The Soccer Tournament Revisited Properties of Combinations Special Case of the Inclusion and Exclusion Formula Alternating Sums of CombinationsIII. Combinatorial Problems with Restrictions Lions and Tigers Construction of a Staircase A Bookshelf Knights of the Round Table A Girl Has a Date A Telepathic Séance Derangements Subfactorials Caravan in the Desert On the Merry-Go-Round Queue at the Box Office Problem of Two Rows Additional Properties of CombinationsIV. Distributions and Partitions A Domino Game Putting Things in Boxes A Bouquet The Number of Divisors Picking Apples Picking Mushrooms Sending Photographs Flags on Masts Count of All Signals Various Statistics Partitions of Numbers Mailing of Printed Matter The General Postage Problem Combinatorial Problems in Information Theory Problem of the University Applicant Paying for a Purchase Purchase of Candy Getting Change (Unordered) Partitions of an Integer Use of Graphs Dual Graphs Euler's FormulaV. Combinatorics on a Chessboard Walking in a Town The Arithmetical Square Figurate Numbers Arithmetical Triangle The Extended Arithmetical Triangle Chess King The Generalized Arithmetical Triangle Generalized Arithmetical Triangles and Numbers to the Base m Some Properties of the Numbers Cm(k, n) Checker in a Corner The Arithmetical Pentagon Geometric Proofs of Properties of Combinations Random Walk Brownian Motion In the Realm of the Tsarina of Shemakhan An Absorbing Wall Roaming on an Infinite Plane The General Rook Problem Symmetric Arrangements Two KnightsVI. Recurrence Relations Fibonacci Numbers Another Method of Proof Successive Partitions Multiplication and Division of Numbers Polygon Problems The Head Steward Faces a Difficulty Lucky Bus Ticket Numbers Recurrent Tables Another Solution of the Problem of the Chief Steward Solution of Recurrence Relations Linear Recurrence Relations with Constant Coefficients The Case of Equal Roots of the Characteristic Equation Application of the Theory of Recurrence Relations to Information Theory Third Solution of the Problem of the Chief StewardVII. Combinatorics and Series Division of Polynomials Algebraic Fractions and Power Series Operations on Power Series Application of Power Series to Proofs of Identities Generating Functions The Binomial Expansion The Multinomial Expansion The Binomial Series Expansion Computation of Square Roots Generating Functions and Recurrence Relations Decomposition into Elementary Fractions (Partial Fraction Decomposition) On a Certain Nonlinear Recurrence Relation Generating Functions and Partitions of Numbers Summary of Results on Combinatorial DistributionsVIII. Problems in CombinatoricsAnswers and HintsIndex