By Richard P. Stanley

Catalan numbers are essentially the most ubiquitous series of numbers in arithmetic. This e-book provides for the 1st time a finished selection of their houses and functions to combinatorics, algebra, research, quantity concept, chance concept, geometry, topology, and different components. Following an advent to the fundamental homes of Catalan numbers, the publication provides 214 other kinds of items counted via them within the type of routines with recommendations. The reader can attempt fixing the workouts or just flick through them. a few sixty eight extra workouts with prescribed hassle degrees current numerous houses of Catalan numbers and comparable numbers, resembling Fuss-Catalan numbers, Motzkin numbers, Schröder numbers, Narayana numbers, large Catalan numbers, q-Catalan numbers and (q,t)-Catalan numbers. The ebook ends with a heritage of Catalan numbers by means of Igor Pak and a word list of key phrases. even if your curiosity in arithmetic is sport or learn, you will discover lots of interesting and stimulating proof here.

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Catalan Numbers by Richard P. Stanley

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