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Lie Algebras and the Four Color Theorem

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abstract

We present a ``reasonable'' statement about Lie algebras that is equivalent to the Four Color Theorem. The notions appearing in the statement also appear in the theory of finite-type invariants of knots (Vassiliev invariants) and 3-manifolds.

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2026 1

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Categorification of some Penrose polynomials

math.CO · 2026-07-02 · unverdicted · novelty 5.0

Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.

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  • Categorification of some Penrose polynomials math.CO · 2026-07-02 · unverdicted · none · ref 6 · internal anchor

    Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.