An integer partition of a positive integer n is an unordered sum of positive integers adding up to n. For instance, there are 5 partitions of 4 which are 4, 3+1, 2+2, 2+1+1, 1+1+1+1. Since we reqired the sums tı be unordered, 1+3 is not registered as another partition.

Cylindrical partitions are defined by Gessel and Krattenthaler [1], and they are lists of partitions satisfying additional constraints. Cylindric partitions have received much attention lately in literature.

In this project, the students will study integer partitions from a combinatorial perspective first. Then, they will examine some existing algorithms to generate integer partitions to adapt them to generate cylindric partitions. Then, they will develop another program for various visualizations of cylindric partitions.

[1] Gessel, I. and Krattenthaler, C., 1997. Cylindric partitions. Transactions of the American Mathematical Society, 349(2), pp.429-479.

### About Project Supervisors

Kağan Kurşungöz, http://people.sabanciuniv.edu/~kursungoz/ , kursungoz@sabanciuniv.edu