Challenging Mathematical Problems with Elementary Solutions: Combinatorial analysis and probability theoryHolden-Day, 1964 |
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第 1 到 3 筆結果,共 16 筆
第 3 頁
... called combinatorial , as they are exercises in calculating the number of different combinations of various objects . The branch of mathematics which deals with such problems is called combinatorial analysis . In the solutions to many ...
... called combinatorial , as they are exercises in calculating the number of different combinations of various objects . The branch of mathematics which deals with such problems is called combinatorial analysis . In the solutions to many ...
第 9 頁
... called partitions of n , and the terms are called parts . 32a . * Prove that the number of partitions of n into at most m parts is equal to the number of partitions of n whose parts are all ≤ m . For example , if n = 5 and m = 3 , the ...
... called partitions of n , and the terms are called parts . 32a . * Prove that the number of partitions of n into at most m parts is equal to the number of partitions of n whose parts are all ≤ m . For example , if n = 5 and m = 3 , the ...
第 72 頁
... called the Ferrars graph of the given partition # . If the graph is read by columns instead of rows we obtain a new partition ' of n , called the conjugate of . For example , the figure above shows that the conjugate of 5 + 2 + 2 + 1 is ...
... called the Ferrars graph of the given partition # . If the graph is read by columns instead of rows we obtain a new partition ' of n , called the conjugate of . For example , the figure above shows that the conjugate of 5 + 2 + 2 + 1 is ...
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A₁ A₂ An+m arrangements b₁ B₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula G₁ given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks S₁ segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose T₂ total number triangle unfavorable values vertex vertices