Cameron–Liebler line classes of PG(3,q) admitting PGL(2,q)

Cossidente, Antonio; Pavese, Francesco

doi:10.1016/j.jcta.2019.04.004

Cited by 10 publications

(7 citation statements)

References 16 publications

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“…Many nontrivial (and nonisomorphic) examples of Cameron-Liebler line classes have been found recently (see [8,[11][12][13]24]), which thus give rise to various examples of perfect sets in the corresponding graphs of MOLS.…”

Section: Mutually Orthogonal Latin Squaresmentioning

confidence: 99%

“…A straightforward calculation shows that it is a

(q^{2} - q - 1)

‐perfect set, whereas the graph

Σ

, which is the bilinear‐forms graph

{Bil}_{q} (2 \times 2)

(see, eg, [7, Section 9.5.A]), can be viewed as a graph of

q - 1

MOLS of order

q^{2}

. Many nontrivial (and nonisomorphic) examples of Cameron–Liebler line classes have been found recently (see ), which thus give rise to various examples of perfect sets in the corresponding graphs of MOLS.…”

Section: Mutually Orthogonal Latin Squaresmentioning

confidence: 99%

See 1 more Smart Citation

Equitable partitions of Latin‐square graphs

Bailey

Cameron

Gavrilyuk

et al. 2018

J of Combinatorial Designs

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Section: Mutually Orthogonal Latin Squaresmentioning

confidence: 99%

“…A straightforward calculation shows that it is a

(q^{2} - q - 1)

‐perfect set, whereas the graph

Σ

, which is the bilinear‐forms graph

{Bil}_{q} (2 \times 2)

(see, eg, [7, Section 9.5.A]), can be viewed as a graph of

q - 1

MOLS of order

q^{2}

Section: Mutually Orthogonal Latin Squaresmentioning

confidence: 99%

Equitable partitions of Latin‐square graphs

Bailey

Cameron

Gavrilyuk

et al. 2018

J of Combinatorial Designs

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show abstract

“…Note that via the field reduction [18] one can construct tight sets of Q + (6b − 1, q) from a variety of those of Q + (5, q b ) that have been discovered recently [7,8,9,10,14,15]. Thus, Q + (7, q) and Q + (9, q) seem to be the first unexplored cases, where we are not aware of any non-trivial tight sets.…”

Section: Introductionmentioning

confidence: 98%

On tight sets of hyperbolic quadrics

Gavrilyuk¹

2019

Preprint

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We prove that the parameter x of a tight set T of a hyperbolic quadric Q + (2n + 1, q) of an odd rank n + 1 satisfies x 2 + w(w − x) ≡ 0 mod q + 1, where w is the number of points of T in any generator of Q + (2n + 1, q). As this modular equation should have an integer solution in w if such a T exists, this condition rules out roughly at least one half of all possible parameters x. It generalizes a previous result by the author and K. Metsch shown for tight sets of a hyperbolic quadric Q + (5, q) (also known as Cameron-Liebler line classes in PG(3, q)).

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“…These line classes were later called Cameron-Liebler line sets in their honor. Many characterisation and classification results about Cameron-Liebler sets were obtained (see [6,12,15,26,30,31,32,39,40,46] amongst others). The many equivalent ways to describe a Cameron-Liebler set, both algebraically and combinatorially, sparked the interest of many researchers, and allowed for generalisations.…”

Section: Introductionmentioning

confidence: 99%

Equivalent definitions for (degree one) Cameron–Liebler classes of generators in finite classical polar spaces

Boeck

D'haeseleer

2020

Discrete Mathematics

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In this article, we study degree one Cameron-Liebler sets of generators in all finite classical polar spaces, which is a particular type of a Cameron-Liebler set of generators in this polar space, [9]. These degree one Cameron-Liebler sets are defined similar to the Boolean degree one functions, [15]. We summarize the equivalent definitions for these sets and give a classification result for the degree one Cameron-Liebler sets in the polar spaces W (5, q) and Q(6, q).

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Cameron–Liebler line classes of PG(3,q) admitting PGL(2,q)

Cited by 10 publications

References 16 publications

Equitable partitions of Latin‐square graphs

Equitable partitions of Latin‐square graphs

On tight sets of hyperbolic quadrics

Equivalent definitions for (degree one) Cameron–Liebler classes of generators in finite classical polar spaces

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