The Fibonacci partition triangles
type: Item
instance of: scholarly article
title: The Fibonacci partition triangles
zbMATH Open document ID: 1276.11022
author: Philipp Fahr
author: Claus Michael Ringel
published in: Advances in Mathematics
publication date: 2012-07-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.2849
review text: Building on their earlier work on quivers (directed graphs), in particular, the representation theory of the 3-Kronecker quivers, the authors here explore partition formulas for the Fibonacci numbers. The resulting two triangles, one for the even-index and the other for the odd-index Fibonacci numbers, resemble the classical Pascal triangle except there is additional additivity along ``hooks''. The numbers along inclined lines are obtained by evaluating polynomials. The resulting triangles of numbers appear at once familiar and strange. The valued translation quivers present are derived from group actions and the 3-regular tree. At the end a further investigation is proposed-exploring the relationship of Delannoy paths and elements of the Fibonacci modules.
reviewed by: Gerald L. Alexanderson
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 11B65
zbMATH DE Number: 6060978
zbMATH Keywords: Fibonacci numbers
zbMATH Keywords: partition formulas
zbMATH Keywords: representations of quivers
zbMATH Keywords: Kronecker quiver
zbMATH Keywords: Fibonacci modules
zbMATH Keywords: 3-regular tree
zbMATH Keywords: Pascal triangle
zbMATH Keywords: additive functions on translation quivers
zbMATH Keywords: valued translation quivers
zbMATH Keywords: left hammocks
zbMATH Keywords: Delannoy paths
MaRDI profile type: Publication
OpenAlex ID: W2016699569
arXiv ID: 1109.2849
cites work: Q4871718
cites work: Q3630295
cites work: Q5387549
cites work: Categorification of the Fibonacci numbers using representations of quivers
cites work: Q3890860
cites work: Q3550088
cites work: Fibonacci and Lucas numbers with applications. Volume I
cites work: Hammocks
DOI: 10.1016/J.AIM.2012.04.010
description: scientific article; zbMATH DE number 6060978