Hydrogen Atom in a Finite Linear Space

2000 ◽  
Vol 160 (1) ◽  
pp. 179-194 ◽  
Author(s):  
Rafael G. Campos ◽  
L.O. Pimentel
Keyword(s):  
Hydrogen Atom ◽  
Linear Space ◽  
Finite Linear Space ◽  
Finite Linear

Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

2017 ◽  
Vol 16 (06) ◽  
pp. 1750110
Author(s):  
Haiyan Guan ◽  
Shenglin Zhou
Keyword(s):  
Linear Space ◽  
Automorphism Groups ◽  
Linear Spaces ◽  
Finite Linear Space ◽  
Transitive Point ◽  
Finite Linear

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let [Formula: see text] be a non-trivial finite linear space with [Formula: see text] points, where [Formula: see text] and [Formula: see text] are two primes. We prove that if [Formula: see text] is line-transitive point-imprimitive, then [Formula: see text] is solvable.

scholarly journals A dual approach to embedding the complement of two lines in a finite projective plane

1991 ◽  
Vol 51 (3) ◽  
pp. 426-435
Author(s):  
Lynn Margaret Batten
Keyword(s):  
Projective Plane ◽  
Linear Space ◽  
Finite Projective Plane ◽  
Exceptional Case ◽  
Subject Classification ◽  
Unique Point ◽  
Dual Approach ◽  
05 B 05 ◽  
Finite Linear Space ◽  
Finite Linear

AbstractLet S be a finite linear space on v ≥ n2 –n points and b = n2+n+1–m lines, m ≧ 0, n ≧ 1, such that at most m points are not on n + 1 lines. If m ≧ 1, except if m = 1 and a unique point on n lines is on no line with two points, then S embeds uniquely in a projective plane of order n or is one exceptional case if n =4. If m ≦ 1 and if v ≧ n2 – 2√n + 3, + 6, the same conclusion holds, except possibly for the uniqueness.1991 Mathematics subject classification (Amer. Math. Soc.) 05 B 05, 51 E 10.

scholarly journals The exceptional case in a theorem of Bose and Shrikhande

1977 ◽  
Vol 24 (1) ◽  
pp. 64-78 ◽  
Author(s):  
Paul de Witte ◽  
Jennifer Seberry Wallis
Keyword(s):  
Projective Plane ◽  
Linear Space ◽  
Finite Projective Plane ◽  
Exceptional Case ◽  
Finite Linear Space ◽  
Finite Linear

AbstractIt is shown that (n being an integer) any non-trivial finite linear space with n2- 1 points, all of degree at most n+1, is embeddable in a finite projective plane of order n. This generalizes a theorem of Bose and Shrikhande and settles the unsolved case n = 6.

scholarly journals Embedding the complement of two lines in a finite projective plane

1976 ◽  
Vol 22 (1) ◽  
pp. 27-34 ◽  
Author(s):  
Jim Totten
Keyword(s):  
Graph Theory ◽  
Projective Plane ◽  
Linear Space ◽  
Finite Projective Plane ◽  
Line Graphs ◽  
Finite Linear Space ◽  
Finite Linear

In this paper we use a result from graph theory on the characterization of the line graphs of the complete bigraphs to show that if n is any integer ≥ 2 then any finite linear space having p = n2 − n or p = n2 − n + 1 points, of which at least n2 − n have degree n + 1, and q ≤ n2 + n − 1 lines is embeddable in an FPP of order n unless n = 4. If n = 4 there is only one possible exception for each of the two values of p, and for p = n2 − n, this exception can be embedded in the FPP of order 5.

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