Introduction to analytic combinatorics

Cyril Nicaud

Laboratoire d’Informatique Gaspard Monge (LIGM), Université Paris-Est, France

Laboratoire d’Informatique Gaspard Monge (LIGM), Université Paris-Est, France

2016/10/19 Wed 4PM-5PM

In classical combinatorics, sequences of positive integers are usually studied through their generating series. These formal power series can be used to classify the sequences, to obtain closed formulas for the number of object of a given size, …

Seeing the generating series as analytic functions, we can use tools of complex analysis (such as the residue theorem) to obtain, typically, an asymptotic equivalent to the sequence under consideration.

In this talk I will give a quick overview of the main results obtained in this field, from the automatic construction of generating series to some theorems coming from the theory of functions of a complex variable.

The talk will not assume any specific knowledge in combinatorics or complex analysis.

Seeing the generating series as analytic functions, we can use tools of complex analysis (such as the residue theorem) to obtain, typically, an asymptotic equivalent to the sequence under consideration.

In this talk I will give a quick overview of the main results obtained in this field, from the automatic construction of generating series to some theorems coming from the theory of functions of a complex variable.

The talk will not assume any specific knowledge in combinatorics or complex analysis.

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