Szego Seminar: "Proportion of Nonunique Zeckendorf Related Partitions in the Lucas Sequence"

Abstract: Zeckendorf’s Theorem states that every natural number can be uniquely partitioned into the sum of distinct and nonconsecutive terms of the Fibonacci sequence. Similarly, every natural number can be partitioned into the sum of distinct and nonconsecutive terms of the Lucas sequence, although such partitions need not be unique. We calculate the limiting value of the proportion of natural numbers that cannot be uniquely partitioned into the sum of distinct and nonconsecutive terms of the Lucas sequence.

Host: Nathan Wagner