JP Journal of Geometry and Topology
Volume 16, Issue 2, Pages 127 - 152
(November 2014)
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THE CORRELATIONS OF FINITE DESARGUESIAN PLANES OF EVEN SQUARE ORDER DEFINED BY UPPER TRIANGULAR MATRICES WITH FOUR NONZERO ENTRIES
Barbu C. Kestenband
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Abstract: The present article continues the classification of the correlations of an even prime number.
As in the case in which q is odd, some matrices with four nonvanishing entries are equivalent to diagonal matrices. When this equivalence does not take place, a correlation defined by an upper triangular matrix with four nonzero entries, with companion automorphism where can have the following numbers of absolute points:
or or for n odd,
or or for n even.
We also discuss the equivalence classes into which these correlations fall, as well as the configurations of their sets of absolute points. |
| Keywords and phrases: companion automorphism, absolute set of a correlation, equivalence, residue class, full secant, short secant. |
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