منابع مشابه
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...
متن کاملOn 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...
متن کاملCameron-Liebler line classes in PG(n, 4)
We derive a new existence condition for Cameron – Liebler line classes in PG(3, q). As an application, we obtain the characterization of Cameron – Liebler line classes in PG(n, 4), n ≥ 3.
متن کاملA 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...
متن کاملA modular equality for Cameron-Liebler line classes
In this paper we prove that a Cameron-Liebler line class L in PG(3, q) with parameter x has the property that ( x 2 ) +n(n−x) ≡ 0 mod q+1 for the number n of lines of L in any plane of PG(3, q). It follows that the modular equation ( x 2 ) + n(n − x) ≡ 0 mod q + 1 has an integer solution in n. This result rules out roughly at least one half of all possible parameters x. As an application of our...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2020
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2020.101706