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
Balls in boxes and multisets 2
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Reviews
Aug 22, 2017
Great lectures and content. I really enjoyed it. However, the solutions exercises could be clearer and in more detail. Thank you!
Apr 21, 2017
Very good gourse, I persoally enjoyed the lectures in which the relatipnship with other areas of mathematics were discussed.
From the lesson
Binomial coefficients, continued. Inclusion and exclusion formula.
In the first part of this lecture we will see more applications of binomial coefficients, in particular, their appearance in counting multisets. The second part is devoted to the principle of inclusion and exclusion: a technique which allows us to find the number of elements in the union of several sets, given the cardinalities of all of their intersections. We discuss its applications to various combinatorial problem, including the computation of the number of permutations without fixed points (the derangement problem).
Taught By
Evgeny Smirnov
Associate Professor
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