On a Conjecture of Cameron and Liebler

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On Cameron–Liebler line classes

Cameron–Liebler line classes are sets of lines in PGð3; qÞ that contain a fixed number x of lines of every spread. Cameron and Liebler classified them for x A f0; 1; 2; q 1; q; q þ 1g and conjectured that no others exist. This conjecture was disproven by Drudge and his counterexample was generalised to a counterexample for any odd q by Bruen and Drudge. Nonexistence of Cameron–Liebler line clas...

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Cameron-Liebler line classes

New examples of Cameron-Liebler line classes in PG(3,q) are given with parameter 1 2 (q 2− 1). These examples have been constructed for many odd values of q using a computer search, by forming a union of line orbits from a cyclic collineation group acting on the space. While there are many equivalent characterizations of these objects, perhaps the most significant is that a set of lines L in PG...

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A non-existence result on Cameron-Liebler line classes

Cameron-Liebler line classes are sets of lines in PG(3, q) that contain a fixed number x of lines of every spread. Cameron and Liebler classified Cameron-Liebler line classes for x ∈ {0, 1, 2, q2 − 1, q2, q2 + 1} and conjectured that no others exist. This conjecture was disproven by Drudge for q = 3 [8] and his counterexample was generalised to a counterexample for any odd q by Bruen and Drudge...

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ژورنال

عنوان ژورنال: European Journal of Combinatorics

سال: 1999

ISSN: 0195-6698

DOI: 10.1006/eujc.1998.0265