Now, you are a math and physics teacher, and you are training a student to retrieve papers. Please provide 10 queries to your student, and you expect your student can find this paper. Here is the abstract:
"In this paper, we use a simple discrete dynamical model to study integer partitions and their lattice. The set of reachable configurations of the model, with the order induced by the transition rule defined on it, is the lattice of all partitions of an integer, equipped with a dominance ordering. We first explain how this lattice can be constructed by an algorithm in linear time with respect to its size by showing that it has a self-similar structure. Then, we define a natural extension of the model to infinity, which we compare with the original lattice. Using a self-similar tree, we obtain an encoding of the obtained lattice which makes it possible to enumerate easily and efficiently all the partitions of a given integer. This approach also gives a recursive formula for the number of partitions of an integer, and some information on special sets of partitions, such as length-bounded partitions."  
Example:
1. What are the limitations of the self-similar dynamical model to study integer partitions?
2. How is the lattice of integer partitions encoded using a self-similar tree?
3. What is discrete dynamical model?
Your Queries used to retrieve this paper:
1.  Limit your response to 550 words.
user