Optimal pebbling of complete binary trees and a meta-Fibonacci sequence
Thomas M. Lewis, Fabian Salinas
TL;DR
This paper introduces a novel method for calculating the optimal pebbling number of complete binary trees and uncovers a surprising link to the Conolly-Fox meta-Fibonacci sequence.
Contribution
The paper presents a new approach for determining optimal pebbling numbers and establishes a connection to a specific meta-Fibonacci sequence, advancing understanding in graph pebbling.
Findings
New method for optimal pebbling number calculation
Connection between binary trees and Conolly-Fox sequence
Potential implications for combinatorial optimization
Abstract
In this paper, we present a new method for determining the optimal pebbling number of a complete binary tree. This method reveals a curious connection between the optimal pebbling numbers of complete binary trees and the Conolly-Fox sequence, a type of meta-Fibonacci sequence.
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Taxonomy
TopicsCoding theory and cryptography · semigroups and automata theory · Algorithms and Data Compression