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 کاملLine Bundles, Rational Points and Ideal Classes
In this note, we will use the term “arithmetic variety” for a normal scheme X for which the structure morphism f : X → Spec(Z) is proper and flat. Let V be a proper, normal (not necessarily geometrically connected) variety over Q. Let us choose a normal model for V over Z, that is an arithmetic variety X whose generic fiber is identified with V . Suppose that F is a number field and consider th...
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...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2011
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-011-9581-2