Una dimostrazione unificata dei teoremi di Bridges e De Witte e del teorema fondamentale degli spazi lineari finiti

摘要

A well known result on finite linear spaces due to de Bruijn and Erdös states that the numberb of lines is greater than or equal to the numberv of points, withb=v if and only if the linear space is either a near pencil, or a projective plane. The problem of characterizing finite linear spaces with small deficienciess=b−v has been investigated by several authors, especially by Bridges forb=v+1 and de Witte forb=v+2.