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The Beauty of Roots

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arxiv 2310.00326 v1 pith:E5IM3PVL submitted 2023-09-30 math.HO math.CO

classification math.HOmath.CO
keywords littlewoodpolynomialrootsalongargumentbeautifulbeautybeen
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A "Littlewood polynomial" is a polynomial whose coefficients are all 1 or -1. The set of all complex roots of all Littlewood polynomials exhibits many complicated, beautiful and fascinating patterns. Some fractal regions of this set closely resemble "dragon sets" formed by iterated function systems. A heuristic argument for this is known, but no precise theorem along these lines has been proved. We invite the reader to try.

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  1. Quantum topology without topology

    math.QA 2025-06 unverdicted novelty 2.0 of 10

    A draft of lecture notes presenting quantum invariants as functors from diagrammatically presented categories, aiming to develop quantum topology without topological input.

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