The polarities of the partial geometry pg(5,5,2) (Q1074857)

In a partial geometry pg(s,t,u) each line is incident with \(s+1\) points, each point is incident with \(t+1\) lines and, for a point X and a line d not incident with X, there are exactly u points on d joined by lines with X. A polarity f is a one to one involutive mapping of the points on the lines and of the lines on the points which preserves the incidence. A point X is ''absolute'' for f if X is incident with \(X^ f\). Here, first is presented an improvement of the lower bound of the number a(f) of absolute points of a polarity f when \(t=s\) and u is odd. Then, the polarities of pg(5,5,2) are classified and their absolute points put in evidence.