2018
DOI: 10.1002/jcd.21625
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Cameron‐Liebler line classes in PG(3, 5)

Abstract: We complete a classification of Cameron-Liebler line classes in PG(3, 5) and show in a uniform way all nonexistence results for those in q PG(3, ), ≤ q 5. K E Y W O R D S Cameron-Liebler line class, equitable partition, Grassmann graph, tight set J Combin Des. 2018;26:563-580. wileyonlinelibrary.com/journal/jcd

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Cited by 6 publications
(3 citation statements)
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References 22 publications
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“…For a point p we define p + (S) = 1 p∈S and p − (S) = 1 p / ∈S , and for a hyperplane π we define π + (S) = 1 S⊆π and π − (S) = 1 S π . The following was shown by Drudge for q = 3 [17, Theorem 6.4]; by Gavrilyuk and Mogilnykh for q = 4 [35, Theorem 3]; and by Gavrilyuk and Matkin [32,45] for q = 5; the result for q = 2 follows easily from [17, Theorem 6.2]: Theorem 1.3 (Drudge, Gavrilyuk and Mogilnykh, Gavrilyuk and Matkin). Let q ∈ {2, 3, 4, 5} and either (a) n ≥ 5 or (b) n = 4 and q = 2.…”
mentioning
confidence: 99%
“…For a point p we define p + (S) = 1 p∈S and p − (S) = 1 p / ∈S , and for a hyperplane π we define π + (S) = 1 S⊆π and π − (S) = 1 S π . The following was shown by Drudge for q = 3 [17, Theorem 6.4]; by Gavrilyuk and Mogilnykh for q = 4 [35, Theorem 3]; and by Gavrilyuk and Matkin [32,45] for q = 5; the result for q = 2 follows easily from [17, Theorem 6.2]: Theorem 1.3 (Drudge, Gavrilyuk and Mogilnykh, Gavrilyuk and Matkin). Let q ∈ {2, 3, 4, 5} and either (a) n ≥ 5 or (b) n = 4 and q = 2.…”
mentioning
confidence: 99%
“…, q n 2 −k+1 } as stated in the abstract. For n ≥ 3k − 4, this simplifies further to Cameron-Liebler classes are completely classified for q ∈ {2, 3, 4, 5} [7,12,18,20], while in general only some limited characterizations are known. For the special case of (n, k) = (4, 2) Gavrilyuk and Metsch [20], and Metsch [27] showed highly non-trivial existence conditions.…”
Section: Introductionmentioning
confidence: 99%
“…See Section 2 for a description of the other known infinite families of Cameron-Liebler line classes with parameter (q 2 + 1)/2. For non-existence and classification results of Cameron-Liebler line classes we refer the reader to [12], [14], [10].…”
mentioning
confidence: 99%