This dissertation is based on three di erent combinatorial papers:
1. The rst paper is by Silvia Heubach and Tou k Mansour: Enumeration of 3-Letter Patterns
in Compositions. Combinatorial Number Theory in Celebration of the 70-th Birthday of
Ronald Graham. In: De Gruyter Proceedings in Mathematics. 243-264, (2007).
2. The second paper is by Daniel J. Velleman and Gregory S. Warrington: What to expect
in a game of memory. American Mathematical Monthly, 120:787-805 (2013).
3. The third paper is by Mireille Bousquet-M elou and Richard Brak: Exactly Solved Models
of Polyominoes and Polygons. Polygons, Polyominoes and Polycubes. In: Lecture Notes in
Physics, 775:43-78, (2009).
