Characteristic Polynomials of Hyperplane Arrangements via Finite Fields and Tutte Specialization — E8 Intelligence Research

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The characteristic polynomial of a hyperplane arrangement can be computed using finite field methods to encode its combinatorial structure, and the Tutte polynomial of a symmetric arrangement specializes to this characteristic polynomial, linking root systems to chromatic and flow polynomials. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22294660

September 4, 2026Open Access

Characteristic Polynomials of Hyperplane Arrangements via Finite Fields and Tutte Specialization — E8 Intelligence Research

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Key Points

Determine the characteristic polynomials of hyperplane arrangements using finite field enumeration and examine their relationship to Tutte polynomial specializations.
Calculated arrangement complements over finite fields using point-counting methods.
Applied Möbius inversion over intersection lattices to construct characteristic polynomials.
Derived polynomial factorizations for reflection hyperplane arrangements associated with Weyl groups across classical root systems.
Demonstrated that characteristic polynomials evaluated at prime powers directly yield the point count of hyperplane arrangement complements in finite vector spaces.
Factored characteristic polynomials of reflection arrangements into products of linear terms defined by Weyl group exponents.

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Implication

Theoretical analysis demonstrates finite field methods determine characteristic polynomials in hyperplane arrangements, linking Tutte polynomials and root systems to algebraic combinatorics.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9d1e3328139818eab20f65 https://doi.org/10.5281/zenodo.22294660

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Characteristic Polynomials of Hyperplane Arrangements via Finite Fields and Tutte Specialization — E8 Intelligence Research

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Characteristic Polynomials of Hyperplane Arrangements via Finite Fields and Tutte Specialization — E8 Intelligence Research

Key Points

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Implication

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