Notes on Combinatorics - QMUL Maths

Notes on CombinatoricsPeter J. CameroniiPreface: What is Combinatorics ? Combinatorics , the mathematics of patterns, .. , helps us design com-puter networks, crack security codes, or solve sudokusUrsula Martin, Vice-Principal (Science and Engineering),Queen Mary, University of LondonThese Notes accompanied the course MAS219, Combinatorics , at Queen Mary,University of London, in the Autumn semester is impossible to define Combinatorics , but an approximate description wouldgo like this. We are given the job of arranging certain objects or items accordingto a specified pattern. Some of the questions that arise include: Is the arrangement possible? In how many ways can the arrangement be made? How do we go about finding such an arrangement?This is best illustrated by 1: SudokuYou are given a 9 9 grid, divided into nine 3 3 job is to put the numbers 1,2,..,9 into the cells of the grid in such a waythat each number occurs just once in each row, once in each column, and once ineach 3 3 is not hard to see that the arrangement is indeed possible.

ii Preface: What is Combinatorics? Combinatorics, the mathematics of patterns, ..., helps us design com-puter networks, crack security codes, or solve sudokus

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