On a Conjecture of Cameron and Liebler

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...

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...

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...

The Cameron-Liebler problem for sets

On the Cameron-Praeger conjecture

This paper takes a significant step towards confirming a long-standing and far-reaching conjecture of Peter J. Cameron and Cheryl E. Praeger. They conjectured in 1993 that there are no nontrivial block-transitive 6-designs. We prove that the Cameron-Praeger conjecture is true for the important case of non-trivial Steiner 6-designs, i.e. for 6-(v, k, λ) designs with λ = 1, except possibly when t...