How to count leaves in the trees from Tetris? E´lise Vandomme Postdoc at the LaCIM (UQAM) Colloque panqu´eb´ecois des ´etudiants de l’ISM Trois-Rivi`eres – May 2017 1/31 2/31 Trees in Tetris 3/31 Trees in Tetris 3/31 Trees in Tetris 3/31 Polyomino A polyomino is a connected union of unit squares, called cells. 4/31 Solomon W. Golomb (1932 - 2016) 5/31 Domino: Tromino: Tetromino: How many polyominoes with n cells? Unknown for n ≥ 57 Combinatorial Problems Monomino: 6/31 Tromino: Tetromino: How many polyominoes with n cells? Unknown for n ≥ 57 Combinatorial Problems Monomino: Domino: 6/31 Tetromino: How many polyominoes with n cells? Unknown for n ≥ 57 Combinatorial Problems Monomino: Domino: Tromino: 6/31