Cell Patterns in Integer Partitions
Toufik Mansour, Armend Sh. Shabani, Daniel Yaqubi · Journal of automata, languages and combinatorics · 2019
A partition of a positive integer $n$ is a finite nonincreasing sequence of positive integers whose sum is $n$. Integer partitions can be graphically represented through Ferrers diagrams (graphs). These diagrams may contain smaller partitions, defined as cell patterns. In this paper, we study the number of different types of cell patterns lying entirely in partitions of $n$. Using the generating functions method we will enumerate integer partitions according to cell patterns of several types.