ترکیبیات

Combinatorics deals with simple combinatorial problems, recurrence relations, and generating functions, particularly the binomial expansions. The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions. The text also explains ordered or unordered partitions of numbers, geometric methods, random walk problems, and variants of the arithmetical triangle. One example of the use of combinatorics is the choice of the number 3 in the genetic code. Another example involves the choice of crew for a spaceship where it is necessary to consider the psychological conditions of the applicants for space travel. The text also investigates the sieve of Erastothenes whose problem concerns finding all the primes in the sequence of natural numbers from 1 to N. The book also tackles the application of power series to proof of identities, the binomial series expansion, decomposition into elementary fractions, and nonlinear recurrence relation. The book can be highly educational and interesting to students or academicians involved in mathematics, algebra, and statistics. Contents......Page all_6194_to_00314.cpc0005.djvu Foreword......Page all_6194_to_00314.cpc0009.djvu Preface to the Russian Edition......Page all_6194_to_00314.cpc0011.djvu Superstitious Cyclists......Page all_6194_to_00314.cpc0017.djvu Samples with Repetitions......Page all_6194_to_00314.cpc0018.djvu Systems of Numeration......Page all_6194_to_00314.cpc0019.djvu The Morse Code......Page all_6194_to_00314.cpc0020.djvu Electronic Computers......Page all_6194_to_00314.cpc0021.djvu General Rules of Combinatorics......Page all_6194_to_00314.cpc0022.djvu A Domino Problem......Page all_6194_to_00314.cpc0024.djvu Crew of a Spaceship......Page all_6194_to_00314.cpc0025.djvu A Checkers Problem......Page all_6194_to_00314.cpc0026.djvu How Many People Do Not Know a Foreign Language?......Page all_6194_to_00314.cpc0028.djvu The Principle of Inclusion and Exclusion......Page all_6194_to_00314.cpc0030.djvu The Sieve of Erastothenes......Page all_6194_to_00314.cpc0032.djvu Samples without Repetitions......Page all_6194_to_00314.cpc0034.djvu Permutations......Page all_6194_to_00314.cpc0035.djvu A Rook Problem......Page all_6194_to_00314.cpc0036.djvu Linguistic Problems......Page all_6194_to_00314.cpc0037.djvu Dancing in a Circle......Page all_6194_to_00314.cpc0038.djvu Permutations with Repetitions......Page all_6194_to_00314.cpc0039.djvu Anagrams......Page all_6194_to_00314.cpc0040.djvu Combinations......Page all_6194_to_00314.cpc0042.djvu The Genoa Lottery......Page all_6194_to_00314.cpc0044.djvu Buying Pastry......Page all_6194_to_00314.cpc0047.djvu Combinations with Repetitions......Page all_6194_to_00314.cpc0048.djvu The Soccer Tournament Revisited......Page all_6194_to_00314.cpc0049.djvu Properties of Combinations......Page all_6194_to_00314.cpc0050.djvu Alternating Sums of Combinations......Page all_6194_to_00314.cpc0056.djvu Lions and Tigers......Page all_6194_to_00314.cpc0059.djvu Construction of a Staircase......Page all_6194_to_00314.cpc0060.djvu A Bookshelf......Page all_6194_to_00314.cpc0061.djvu Knights of the Round Table......Page all_6194_to_00314.cpc0062.djvu A Girl Has a Date......Page all_6194_to_00314.cpc0063.djvu A Telepathic Séance......Page all_6194_to_00314.cpc0065.djvu Derangements......Page all_6194_to_00314.cpc0067.djvu Subfactorials......Page all_6194_to_00314.cpc0068.djvu Caravan in the Desert......Page all_6194_to_00314.cpc0070.djvu On the Merry-Go-Round......Page all_6194_to_00314.cpc0072.djvu Queue at the Box Office......Page all_6194_to_00314.cpc0073.djvu Problem of Two Rows......Page all_6194_to_00314.cpc0076.djvu Additional Properties of Combinations......Page all_6194_to_00314.cpc0077.djvu A Domino Game......Page all_6194_to_00314.cpc0080.djvu A Bouquet......Page all_6194_to_00314.cpc0082.djvu The Number of Divisors......Page all_6194_to_00314.cpc0083.djvu Picking Apples......Page all_6194_to_00314.cpc0084.djvu Sending Photographs......Page all_6194_to_00314.cpc0085.djvu Flags on Masts......Page all_6194_to_00314.cpc0086.djvu Count of All Signals......Page all_6194_to_00314.cpc0087.djvu Partitions of Numbers......Page all_6194_to_00314.cpc0088.djvu Mailing of Printed Matter......Page all_6194_to_00314.cpc0089.djvu The General Postage Problem......Page all_6194_to_00314.cpc0090.djvu Combinatorial Problems in Information Theory......Page all_6194_to_00314.cpc0091.djvu Problem of the University Applicant......Page all_6194_to_00314.cpc0092.djvu Paying for a Purchase......Page all_6194_to_00314.cpc0093.djvu Purchase of Candy......Page all_6194_to_00314.cpc0095.djvu Getting Change......Page all_6194_to_00314.cpc0096.djvu Unordered) Partitions of an Integer......Page all_6194_to_00314.cpc0097.djvu Use of Graphs......Page all_6194_to_00314.cpc0098.djvu Dual Graphs......Page all_6194_to_00314.cpc0100.djvu Euler's Formula......Page all_6194_to_00314.cpc0102.djvu Walking in a Town......Page all_6194_to_00314.cpc0106.djvu The Arithmetical Square......Page all_6194_to_00314.cpc0107.djvu Figurate Numbers......Page all_6194_to_00314.cpc0108.djvu Arithmetical Triangle......Page all_6194_to_00314.cpc0109.djvu The Extended Arithmetical Triangle......Page all_6194_to_00314.cpc0111.djvu The Generalized Arithmetical Triangle......Page all_6194_to_00314.cpc0113.djvu Generalized Arithmetical Triangles and Numbers to the Base m......Page all_6194_to_00314.cpc0114.djvu Some Properties of the Numbers Cm(k,n)......Page all_6194_to_00314.cpc0115.djvu Checker in a Corner......Page all_6194_to_00314.cpc0116.djvu The Arithmetical Pentagon......Page all_6194_to_00314.cpc0118.djvu Geometric Proofs of Properties of Combinations......Page all_6194_to_00314.cpc0120.djvu Random Walk......Page all_6194_to_00314.cpc0122.djvu Brownian Motion......Page all_6194_to_00314.cpc0124.djvu In the Realm of the Tsarina of Shemakhan......Page all_6194_to_00314.cpc0125.djvu An Absorbing Wall......Page all_6194_to_00314.cpc0126.djvu Roaming on an Infinite Plane......Page all_6194_to_00314.cpc0127.djvu The General Rook Problem......Page all_6194_to_00314.cpc0128.djvu Symmetric Arrangements......Page all_6194_to_00314.cpc0129.djvu Two Knights......Page all_6194_to_00314.cpc0131.djvu VI. Recurrence Relations......Page all_6194_to_00314.cpc0134.djvu Fibonacci Numbers......Page all_6194_to_00314.cpc0135.djvu Another Method of Proof......Page all_6194_to_00314.cpc0137.djvu Successive Partitions......Page all_6194_to_00314.cpc0138.djvu Multiplication and Division of Numbers......Page all_6194_to_00314.cpc0139.djvu Polygon Problems......Page all_6194_to_00314.cpc0141.djvu The Head Steward Faces a Difficulty......Page all_6194_to_00314.cpc0143.djvu Lucky Bus Ticket Numbers......Page all_6194_to_00314.cpc0146.djvu Recurrent Tables......Page all_6194_to_00314.cpc0147.djvu Another Solution of the Problem of the Chief Steward......Page all_6194_to_00314.cpc0148.djvu Solution of Recurrence Relations......Page all_6194_to_00314.cpc0150.djvu Linear Recurrence Relations with Constant Coefficients......Page all_6194_to_00314.cpc0151.djvu The Case of Equal Roots of the Characteristic Equation......Page all_6194_to_00314.cpc0154.djvu Third Solution of the Problem of the Chief Steward......Page all_6194_to_00314.cpc0155.djvu Division of Polynomials......Page all_6194_to_00314.cpc0157.djvu Algebraic Fractions and Power Series......Page all_6194_to_00314.cpc0158.djvu Operations on Power Series......Page all_6194_to_00314.cpc0162.djvu Application of Power Series to Proofs of Identities......Page all_6194_to_00314.cpc0164.djvu The Binomial Expansion......Page all_6194_to_00314.cpc0166.djvu The Multinomial Expansion......Page all_6194_to_00314.cpc0169.djvu The Binomial Series Expansion......Page all_6194_to_00314.cpc0172.djvu Computation of Square Roots......Page all_6194_to_00314.cpc0174.djvu Generating Functions and Recurrence Relations......Page all_6194_to_00314.cpc0177.djvu Decomposition into Elementary Fractions (Partial Fraction Decomposition)......Page all_6194_to_00314.cpc0178.djvu On a Certain Nonlinear Recurrence Relation......Page all_6194_to_00314.cpc0182.djvu Generating Functions and Partition of Numbers......Page all_6194_to_00314.cpc0183.djvu Summary of Results on Combinatorial Distributions......Page all_6194_to_00314.cpc0187.djvu VIII. Problems in Combinatorics......Page all_6194_to_00314.cpc0189.djvu Answers and Hints......Page all_6194_to_00314.cpc0227.djvu Index......Page all_6194_to_00314.cpc0311.djvu [by] N. Ya. Vilenkin. Translated By A. Shenitzer And S. Shenitzer. Translation Of Kombinatorika.