Fibonacci-like property of partition function

The main result of the paper is the Fibonacci-like property of the partition function. The partition function $p(n)$ has a property: $p(n) \leq p(n-1) + p(n-2)$. Our result shows that if we impose certain restrictions on the partition, then the inequality becomes an equality. Furthermore, we extend this result to cases with a greater number of summands.