Categorification of the Fibonacci numbers using representations of quivers
Philipp Fahr, Claus Michael Ringel
TL;DR
This paper introduces Fibonacci modules that provide a categorification of Fibonacci numbers using representations of specific quivers, extending previous work on even indices to odd indices.
Contribution
It presents a new categorification of Fibonacci numbers through the construction of Fibonacci modules based on quiver representations, covering both even and odd indices.
Findings
Fibonacci modules effectively categorify Fibonacci numbers.
Extension of previous work to include odd-index Fibonacci numbers.
Representation theory offers a new perspective on Fibonacci sequences.
Abstract
In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the 3-regular star. Now we deal in a similar way with the odd-index Fibonacci numbers. The Fibonacci modules introduced here provide a convenient categorification of the Fibonacci numbers.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Mathematical Identities