A Fibonacci variant of the Rogers-Ramanujan identities via crystal energy
Shunsuke Tsuchioka
TL;DR
This paper introduces a new Fibonacci-based variant of the Rogers-Ramanujan identities by defining a length function on perfect crystals, connecting crystal energy with Fibonacci numbers.
Contribution
It presents a novel Fibonacci variant of the Rogers-Ramanujan identities derived through a new length function on perfect crystals.
Findings
Derived a Fibonacci-based Rogers-Ramanujan identity
Connected crystal energy with Fibonacci numbers
Introduced a new length function for perfect crystals
Abstract
We define a length function for a perfect crystal. As an application, we derive a variant of the Rogers-Ramanujan identities which involves (a -analog of) the Fibonacci numbers.
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Taxonomy
TopicsX-ray Diffraction in Crystallography · Advanced Mathematical Identities · Crystallography and molecular interactions