Transcription of Stephan Wagner Version: July 2011 - Stellenbosch …
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CombinatoricsStephan WagnerVersion: july 2011 Contents1 Elementary enumeration Problems ..72 Properties of binomial coefficients, combinatorial The recursion .. The binomial theorem and its applications .. Bijections and the Catalan numbers .. Additional problems ..163 The principle of inclusion and A simple example .. The general formula .. Applications .. Additional problems ..234 Enumeration by means of A first example .. Finding and solving linear recursions .. Generating functions .. Additional problems ..365 The pigeonhole The principle and a first example .. Various applications .. Additional problems ..416 Potential functions and Invariants .. Potential functions .. Additional problems.
Preface These notes are aimed at advanced participants in mathematical olympiads and their coaches. Some of the parts cover more than …
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