Kac--Moody Fibonacci sequences
Number Theory
2026-01-06 v1 Combinatorics
Quantum Algebra
Representation Theory
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.
Keywords
Cite
@article{arxiv.2601.00958,
title = {Kac--Moody Fibonacci sequences},
author = {Lisa Carbone and Pranav Shankar},
journal= {arXiv preprint arXiv:2601.00958},
year = {2026}
}