Enumerative combinatorics deals with finite sets and their cardinalities. In other words, a typical problem of enumerative combinatorics is to find the number of ways a certain pattern can be formed. In the first part of our course we will be dealing with elementary combinatorial objects and notions: permutations, combinations, compositions, Fibonacci and Catalan numbers etc. In the second part of the course we introduce the notion of generating functions and use it to study recurrence relations and partition numbers. The course is mostly self-contained. However, some acquaintance with basic linear algebra and analysis (including Taylor series expansion) may be very helpful. Do you have technical problems? Write to us: coursera@hse.ru
Chain rule. Inverse function theorem
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21 août 2017
Great lectures and content. I really enjoyed it. However, the solutions exercises could be clearer and in more detail. Thank you!
17 nov. 2020
This course is very well put together. The lectures are very clear and cover a wide range of interesting topics in combinatorics.
À partir de la leçon
Generating functions, continued. Generating function of the Catalan sequence
In this lecture we discuss further properties of formal power series. In particular, we prove an analogue of the binomial theorem for an arbitrary rational exponent. We apply this technique to computing the generating function of the sequence of Catalan numbers.
Enseigné par
Evgeny Smirnov
Associate Professor
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