Combinatorics: A Very Short Introduction
How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal)
Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries.
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LibraryThing ReviewUser Review - gottfried_leibniz - LibraryThing
Even though, this is a small introduction book –– I still did not completely understand everything. It seems that some of the concepts need deeper thinking, and reflecting on ideas. If you are into ... Read full review
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affine plane algorithm appears arrangement B E D C balls binary words block design boxes Chapter chessboard choose colourings column Combination rule combinatorial complete bipartite graphs construct contains corresponding count cycle graph David discs dodecahedron enumerator Euler example Fibonacci numbers finite projective plane five four four-colour four-colour problem girls gives graph theory Hamiltonian Hamiltonian graphs hexagons inclusion–exclusion principle Königsberg bridges problem least magic squares mathematician mathematics minimum connector problem multiplication rule NP-complete number of edges number of elements number of possible objects Ordered selection orthogonal latin squares partition numbers Pascal’s triangle pentagon permutations Peter planar plane graph plane of order polyhedra polynomial replicates route selection without repetition selections with repetition shown in Figure solution solve square array squares of order sudoku symbols there’s total number Tower of Hanoi travelling salesman problem trees triple system unordered selections varieties vertex