THE CORRELATIONS OF FINITE DESARGUESIAN PLANES OF EVEN SQUARE ORDER DEFINED BY UPPER TRIANGULAR MATRICES WITH FOUR NONZERO ENTRIES
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.
companion automorphism, absolute set of a correlation, equivalence, residue class, full secant, short secant.