Chris Deugau ; Frank Ruskey - Complete k-ary trees and generalized meta-Fibonacci sequences

dmtcs:3514 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3514
Complete k-ary trees and generalized meta-Fibonacci sequencesArticle

Authors: Chris Deugau 1; Frank Ruskey 1

  • 1 Department of Computer Science [Victoria]

We show that a family of generalized meta-Fibonacci sequences arise when counting the number of leaves at the largest level in certain infinite sequences of k-ary trees and restricted compositions of an integer. For this family of generalized meta-Fibonacci sequences and two families of related sequences we derive ordinary generating functions and recurrence relations.

https://doi.org/10.46298/dmtcs.3514
Source: HAL:hal-01184719v1
Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: Meta-Fibonacci sequence,k-ary tree,recurrence relation,generating function,ruler function.,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]
Funding:
    Source : OpenAIRE Graph
  • Funder: Natural Sciences and Engineering Research Council of Canada

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