The Fibonacci partition triangles
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.
additive functions on translation quivers
scientific article; zbMATH DE number 6060978