Projective planes of infinite but isolic order
1976 ◽
Vol 41
(2)
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pp. 391-404
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Keyword(s):
The main purpose of this paper is to show how partial recursive functions and isols can be used to generalize the following three well-known theorems of combinatorial theory.(I) For every finite projective plane Π there is a unique number n such that Π has exactly n2 + n + 1 points and exactly n2 + n + 1 lines.(II) Every finite projective plane of order n can be coordinatized by a finite planar ternary ring of order n. Conversely, every finite planar ternary ring of order n coordinatizes a finite projective plane of order n.(III) There exists a finite projective plane of order n if and only if there exist n − 1 mutually orthogonal Latin squares of order n.
Keyword(s):
1995 ◽
Vol 38
(1)
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pp. 133-149
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1989 ◽
Vol 41
(6)
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pp. 1117-1123
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Keyword(s):
1971 ◽
Vol 11
(1)
◽
pp. 101-105
2018 ◽
Vol 18
(13&14)
◽
pp. 1152-1164
1988 ◽
Vol 31
(4)
◽
pp. 409-413
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