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September 5, 2025Open Access

Analytical Study of Seven-Dimensional Projective Space

Puntos clave

The research highlights combinatorial properties of the finite projective space of dimension seven, detailing spatial relationships.
Key findings include the relationships between i-spaces and j-spaces, with a focus on intersections and configurations.
An analytical approach was taken to explore properties of the seven-dimensional projective space over a finite field.
This work supports ongoing exploration of projective spaces, emphasizing structural connections among various dimensions.

Resumen

Analytical studies of finite projective spaces of interest make understanding space objects much easier. In this paper, an analytic study is given of the finite projective space of dimension seven. Formulas of some combinatorial properties and details are found like, number of i-spaces through j-spaces, i>j, spaces resulting from the intersection of two spaces, i-space with j-space i≠j, and the relation between lines and skew lines. Also, the basic conditions to spread the space by lines were also found. All obtained results were implemented on the finite projective space of dimension seven over the finite field of order two as an example.

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