Authors :
Jesús Castañeda Rivera
Volume/Issue :
Volume 9 - 2024, Issue 12 - December
Google Scholar :
https://tinyurl.com/2swvrfnd
Scribd :
https://tinyurl.com/2pnhve3n
DOI :
https://doi.org/10.5281/zenodo.14636684
Abstract :
Dual affine spaces are geometries with points
and lines, lines have three points and, at most, a line
passes through two points. Furthermore, we have that its
planes are the duals of the affine plane over the field of
two elements. If the space is connected, numerical
invariants are associated with it. Let n be the number of
points in space and k be the number of points that, given
a fixed point, are not collinear with it. In this research
we characterize the geometric spaces that satisfy the
Desargues property “Every pair of non-collinear points
has exactly four collinear points.” represented by pairs of
numbers (n, k) that satisfy certain algebraic properties
studied by D. Higman (1964), H. Cárdenas (1999, 2001,
2002) and J. Castañeda (2011, 2020).
Keywords :
Dual Affine Space, Desargues Configuration, Numerical Dual Affine Spaces, Desargues Spaces.
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Dual affine spaces are geometries with points
and lines, lines have three points and, at most, a line
passes through two points. Furthermore, we have that its
planes are the duals of the affine plane over the field of
two elements. If the space is connected, numerical
invariants are associated with it. Let n be the number of
points in space and k be the number of points that, given
a fixed point, are not collinear with it. In this research
we characterize the geometric spaces that satisfy the
Desargues property “Every pair of non-collinear points
has exactly four collinear points.” represented by pairs of
numbers (n, k) that satisfy certain algebraic properties
studied by D. Higman (1964), H. Cárdenas (1999, 2001,
2002) and J. Castañeda (2011, 2020).
Keywords :
Dual Affine Space, Desargues Configuration, Numerical Dual Affine Spaces, Desargues Spaces.