Journal of Integer Sequences, Vol. 15 (2012), Article 12.2.1

Categorification of the Fibonacci Numbers Using Representations of Quivers


Philipp Fahr
Brehmstr. 51
D-40239 Düsseldorf
Germany

Claus Michael Ringel
Department of Mathematics
Shanghai Jiao Tong University
Shanghai 200240
P. R. China
and
King Abdulaziz University
P. O. Box 80200
Jeddah
Saudi Arabia

Abstract:

In a previous paper we 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 tree. In this paper 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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(Concerned with sequences A000045 A132262 A147316 A197956 A197957.)

Received May 26 2011; revised version received October 17 2011; December 29 2011. Published in Journal of Integer Sequences, December 29 2011.

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