Zoom Maths Club - Numbers and Recurrent Relations - Dr Oleg Karpenkov
24th April 2021
In this talk, we will discuss several recurrent formulas that appear in the enumeration of various natural objects: (1) Catalan Numbers (chords, brackets, chessboard rook travel);(2) Markov Numbers (building solutions of Markov equation);
(3) Bernoulli-Euler Numbers (Bernoulli snakes and Euler snakes);
(4) Fibonacci Numbers (adding squares along the longest side);
(5) Numbers of $k$-combinations (Pascal's Triangle). These formulas provide a fast way to compute these numbers.