Combinatorics

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Howmanypossiblesudokupuzzlesarethere?Inthelottery,whatisthechancethattwowinningballshaveconsecutivenumbers?WhoinventedPascal’striangle?(itwasnotPascal)Combinatorics,thebranchofmathematicsconcernedwithselecting,arranging,andlistingorcountingcollectionsofobjects,workstoanswerallthesequestions.Datingbacksome3000years,andinitiallyconsistingmainlyofthestudyofpermutationsandcombinations,itsscopehasbroadenedtoincludetopicssuchasgraphtheory,partitionsofnumbers,blockdesigns,designofcodes,andlatinsquares.InthisVeryShortIntroductionRobinWilsongivesanoverviewofthefieldanditsapplicationsinmathematicsandcomputertheory,consideringproblemsfromtheshortestroutescoveringcertainstopstotheminimumnumberofcoloursneededtocolouramapwithdifferentcoloursforneighbouringcountries.ABOUTTHESERIES:TheVeryShortIntroductionsseriesfromOxfordUniversityPresscontainshundredsoftitlesinalmosteverysubjectarea.Thesepocket-sizedbooksaretheperfectwaytogetaheadinanewsubjectquickly.Ourexpertauthorscombinefacts,analysis,perspective,newideas,andenthusiasmtomakeinterestingandchallengingtopicshighlyreadable.