Kac--Moody Fibonacci sequences
Abstract
We summarize known results on how to generate an infinite family of integer sequences from the root lattices of rank 2 Kac--Moody algebras. We compute and tabulate the first twenty entries of a number of these sequences. This provides an overarching framework for a large class of Fibonacci-type integer sequences, evaluations of Chebyshev S and U-polynomials and others.
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