Dot Product Bounds in Galois Rings

David Crosby

Dot Product Bounds in Galois Rings

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arxiv 2207.10051 v1 pith:EZWP2H37 submitted 2022-07-20 math.CO math.MG

David Crosby This is my paper · ORCID

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keywords productconfigurationproblemboundboundsconjectureconsiderdistance

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We consider a problem related to the Erdo\H{o}s Unit Distance Conjecture: How often can a single dot product configuration or a multiple dot product configuration occur over a Galoi Ring? We also find a bound on an inverse vector matrix multiplication problem.

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A Structural Condition on Point Sets with Few Distinct Dot Products
math.CO 2025-10 reject novelty 6.0 of 10

Any point set in the plane with o(n^{3/4}) distinct dot products must contain a line through the origin holding n^{1/2} points whose consecutive distance ratios cluster near 1.

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