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
q-binomial coefficients: definition and first properties
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Bewertungen
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.
21. Aug. 2017
Great lectures and content. I really enjoyed it. However, the solutions exercises could be clearer and in more detail. Thank you!
Aus der Unterrichtseinheit
Gaussian binomial coefficients. “Quantum” versions of combinatorial identities
Our final lecture is devoted to the so-called "q-analogues" of various combinatorial notions and identities. As a general principle, we replace identities with numbers by identities with polynomials in a certain variable, usually denoted by q, that return the original statement as q tends to 1. This approach turns out to be extremely useful in various branches of mathematics, from number theory to representation theory.
Unterrichtet von
Evgeny Smirnov
Associate Professor
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