Generalized Fibonacci numbers and dimer statistics
W. T. Lu, F. Y. Wu
TL;DR
This paper introduces new identities for q-analogue Fibonacci numbers and applies them to derive alternative generating functions for close-packed dimer models on non-orientable surfaces.
Contribution
It presents novel product identities for q-Fibonacci numbers and connects them to dimer statistics on complex surfaces.
Findings
New product identities for q-Fibonacci numbers
Alternative expressions for dimer generating functions
Applications to non-orientable surface models
Abstract
We establish new product identities involving the -analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
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