Discrete Mathematics

Por • 29 dic, 2020 • Sección: Educacion

A. Brini, A. Teolis

.The purpose of the present work is to provide short and supple teaching notes for a 30 hours introductory course on elementary textit{Enumerative Algebraic Combinatorics}. We fully adopt the textit{Rota way} (see, e.g. cite{KY}). The themes are organized into a suitable sequence that allows us to derive any result from the preceding ones by elementary processes. Definitions of textit{combinatorial coefficients} are just by their textit{combinatorial meaning}. The derivation techniques of formulae/results are founded upon constructions and two general and elementary principles/methods:
- The textit{bad element} method (for textit{recursive} formulae). As the reader should recognize, the bad element method might be regarded as a combinatorial companion of the idea of textit{conditional probability}.
- The textit{overcounting} principle (for textit{close form} formulae).
Therefore, textit{no computation} is required in textit{proofs}: textit{computation formulae are byproducts of combinatorial constructions}. We tried to provide a self-contained presentation: the only prerequisite is standard high school mathematics. We limited ourselves to the textit{combinatorial point of view}: we invite the reader to draw the (obvious) textit{probabilistic interpretations}.

arXiv:2012.12691v1 [math.HO]

History and Overview (math.HO); Combinatorics (math.CO)

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