Sets of dying period sets for word length n

1. Dying period sets are defined with respect to the genealogy of period sets, which is a tree that describes how period sets of length $n>2$ are algorithmically derived from their "parent" period set of length $n-1$. The algorithm is incremental, that is given the set of period sets for length $n-1$ it computes all period set of length $n$. In this genealogy, which is a tree, whose root is the unique period set of length $1$. Each node at depth $n$ in the tree represents a unique period set for length $n$. Each node has at most two children. Those nodes at depth $n$ that have no children are said to be dying at length $n$. 2. There exist period sets that never dies, meaning that the genealogy is infinite.