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The non‐existence of Cameron–Liebler line classes with parameter 2 < x ⩽ q
Author(s) -
Metsch Klaus
Publication year - 2010
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq057
Subject(s) - mathematics , line (geometry) , quadrangle , combinatorics , pure mathematics , discrete mathematics , geometry , archaeology , history
In this paper it is proved that Cameron–Liebler line classes with parameter x do not exist when 2 < x ⩽ q . We also give a geometrical‐combinatorial proof of the equivalent properties that can be used to define Cameron–Liebler line classes. Finally, we use the same technique as in this proof to prove a result on partial m ‐covers of the classical parabolic generalized quadrangle.