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| N. Vilenkin, George Yankovsky (translator) — Combinatorial mathematics for recreation |
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| Предметный указатель |
Absorbing barriers 83
Al-Kashi 72 112
Alexandria 20 26
Algebraic fractions 104
Alternating sums of combinations 37
Ambo 29
Amino acids 13
Anagrams 26
Application of the theory of recurrence relations to problems of transmitting information 103
Archimedes 26
Arithmetic hexagon 78
Arithmetic pentagon 78
Arithmetic square 70—72
Arithmetic triangle 72—74
Array(s) of dots 65
Array(s), dual 67
Array(s), normal 66
Array(s), self-dual 67
Barriers, absorbing 83
Base-m number system 75
Base-n system of numeration 11
Bernoulli, Jakob 7 55
Binomial coefficients 73
Binomial theorem 110
Boltzmann, L. 59
Bookshelf problem 40
Bose 59
Bose — Einstein statistics 59
Bouquet of flowers 55
Brownian motion 81
Building a stairway 39
Buying cakes 30
Buying candy 63
Cakes, buying 30
Candy, buying 63
Caravan in the desert 46
Cardano formula 72
Cardano, G. 72
Change, getting 64
Characteristic equation 101
Characteristic equation, equal roots of 102
Chebyshev, P. 55
Checker in the corner 77
Checkerboard problems 16
Chess 70ff
Chess king 74
Coefficients, binomial 73
Combinations 22 27
Combinations with repetitions 31
Combinations, alternating sums of 37
Combinations, new properties of 51
Combinations, properties of 33
Combinations, properties of, geometric proof of 79
Combinatorial mathematics 7
Combinatorial problems of information theory 61
Combinatorial problems with restrictions 39ff
Combinatorics 7
Combinatorics and chess 70ff
Combinatorics and series 104ff
Combinatorics of partitions, summary of 122
Combinatorics, general rules of 9ff 13ff
Composite numbers 20
Computer, "Strela" 12
Computer, electronic digital 12
Convergence of number series 105
Convergence, interval of 106
Crew of spaceship 15
Czar Dadon 82
Decomposition into partial fractions 116
Derangements 44
Derangements, general problem of 44
Diagonal, principal 71
Difficulties of a majordomo 94
Diffusion 82
Dirac see "Fermi — Dirac" statistics"
Divergence of number series 105
Divergent series 105
Dividend 104
Dividing polynomials 104
Divisor 104
DNA 13
Domino problem 15
Dominoes 54
Dual arrays 67
e (the number) 106
Einstein, A. 59
Electronic digital computer 12
Entrance-exams problem 61
Equation, characteristic 101
Equation, equal roots of 102
Eratosthenes 20
Eratosthenes, sieve of 20
Euclid 20
Euler's formula 67
Euler's theorem 66 68
Euler, L. 7 55 67—68
Exclusion see "Principle of" "Formula
Extended arithmetic triangle 73
Extracting square roots 114
Factorial 23
Factorization 56
Fermat, P. 7
Fermi — Dirac statistics 59
fibonacci 89
Fibonacci numbers 89 91 101
Figurate numbers 71 72
Figures, Zener 42
Flags on masts 58
Football championship 22
Football championship again 32
Formula, Cardano 72
Formula, Euler's 67
Formula, inclusion and exclusion 19 37
Fractions, algebraic 104
Fractions, partial, decomposition into 116
Functions, Gaussian 82
Functions, generating 109 116 119
gambling 7
games of chance 7
Gauss, K. 82
Gaussian function 82
General problem of postage stamps 61
General problem of the rooks 84
General rules of combinatorics 13ff
Generalized arithmetic triangle 74 75
Generating functions 109 116 119
Generating functions and partitions of integers 119
genetic code 13
Genoese lottery 29
Geometric proof of properties of combinations 79
Getting change 64
Greatest integer (in) 53
Henry III 27
Hexagon, arithmetic 78
Hipparchus 20
Hooke, R. 26
How many people don't know foreign languages 17
Hunting mushrooms 57
Huygens, Christian 27
inclusion see "Principle of" "Formula
Infinite series 105
Infinite series, sum of 105
Information theory 33
Integers, partitioning 65
Integers, partitions of 59
Integers, partitions of, generating functions and 119
Interval of convergence 106
k-arrangements 9 22
King Arthur's Round Table 40
Knights, two 87
| LANCELOT 40
Languages (How many people don't know foreign languages) 17
Leibniz, G.W. 7 27
Liber Abaci 89
Linear recurrence relations with constant coefficients 100
Linguistic problems 24
Lions and tigers 39
Lottery, Genoese 29
Lottery, number 29
Lotto 7
Lucky trolleybus tickets 96
Mailing packages 60
Mailing photographs 57
Majordomo problem, alternative solution of 98
Majordomo problem, third solution 103
Majordomo, difficulties of (first solution) 94
Mathematics, combinatorial 7
Maxwell — Boltzmann statistics 59
Maxwell, G.G. 59
Mere, Chevalier de 7
Merry-go-round 47
Money, paying 62
Morse code 11
Motion, Brownian 81
Multinomial theorem 111
Multiplying and dividing numbers 92
Mushrooms, hunting 57
New properties of combinations 51
Newton's Binomial Theorem 109
Newton's series 112
Newton, Sir Isaac 26 112
Nicomedes 71
Nonlinear recurrence relation 118
Number "one" 32
Number lottery 29
Number series 105
Number series, convergence of 105
Number series, divergence of 105
number systems 10
Number systems, base-m 75
Number(s),  , properties of 75
Number(s), composite 20
Number(s), e 106
Number(s), Fibonacci 89 91 101
Number(s), figurate 71
Number(s), multiplying and dividing 92
Number(s), prime 20
Number(s), pyramidal 72
Number(s), triangular 71
Number-of-divisors problem 56
Numerical triangle 148
Olympiad, Moscow Mathematics 80
Omar Khayyam 72 112
One 32
Operations on power series 107
Order of recurrence relations 99
Partial fractions, decomposition into 116
Particle statistics 59
Partitioning integers 65
Partitions of integers 59 119
Partitions of integers, generating functions and 119
Partitions, combinatorics of (summary) 122
Partitions, process of successive 91
Pascal's triangle 72
Pascal, B. 7 55 72 112
Paying money 62
Pentagon, arithmetic 78
permutations 22
Permutations of n elements 23
Permutations with repetitions 9ff 22 25
Permutations without repetitions 22
Photographs, mailing 57
Picking apples 56
Placing objects into cells 55
Polygons, problems involving 93
Polynomials, dividing 104
Postage stamps, general problem of 61
Power series 107
Power series, operations on 107
Power series, sum of 107
Power series, use of to prove identities 108
Prime numbers 20
Principal diagonal 71
Principle of inclusion and exclusion 18 19 37
Principle of inclusion and exclusion, particular case of 37
Principle, teakettle 17
Problem des manages 96
Problem(s) of points 7
Problem(s) of the rooks 23 28
Problem(s) of the rooks, general 84
Problem(s) of the two ranks 51
Problem(s), bookshelf 40
Problem(s), checkerboard 16
Problem(s), combinatorial (of information theory) 61
Problem(s), combinatorial (with restrictions) 39ff
Problem(s), derangements (general) 44
Problem(s), des manages (problem des manages) 96
Problem(s), domino 15
Problem(s), entrance-exams 61
Problem(s), general (of the rooks) 84
Problem(s), involving polygons 93
Problem(s), linguistic 24
Problem(s), majordomo, alternative solution 98
Problem(s), majordomo, first solution 95
Problem(s), majordomo, third solution 103
Problem(s), number-of-divisors 56
Problem(s), postage stamps (general) 61
Problem(s), rabbit 89
Product of a series 107
Product, rule of 13 14
Properties of combinations 33
Properties of the numbers 75
Pyramidal numbers 72
Pythagoras 71
Quaterno 29
Queen of Shamakha 82
Queen's realm 82
Quinto 29
Quotient 104
Rabbit problem 89
Random walks 80
Random walks on an infinite plane 84
Recurrence relations 89ff 116
Recurrence relations, application to information transmission 103
Recurrence relations, linear (with constant coefficients) 100
Recurrence relations, nonlinear 118
Recurrence relations, order of 99
Recurrence relations, solution of 99 100
Recurrence relations, solution of, general 100
Recurrence tables 97
Relations, recurrence 89ff 116
Remainder 104
Riordan, John 8
Rooks, problem of 23 28
Roots, square, extracting 114
Round dance 25
Rule of product 13 14
Rule of sum 13
Saturn, ring of 27
Science club 22
Secret lock 11
Self-dual arrays 67
Semaphore 11
Series 104ff
Series, divergent 105
Series, infinite 105
Series, infinite, sum of 105
Series, Newton's 112
Series, number 105
Series, number, convergence of 105
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