Strongly Regular (α, β)-Geometries

“…One such configuration is the Desargues configuration, which is a semipartial geometry for α = 2 and µ = 4 (see Section 3 for the definition). There is another such configuration not belonging to the known generalizations of partial geometries such as semipartial geometries [14,19,15] and strongly regular (α, β)-geometries [27], represented in Figure 1.…”

Section: Srgmentioning

confidence: 99%

“…If α = β, the point graph is not necessarily strongly regular. Geometries with this additional property are called strongly regular (α, β)-geometries and are studied in [27]. An important special case are the semipartial geometries, introduced in [14].…”

Section: Families Of Strongly Regular Configurationsmentioning

confidence: 99%

Strongly regular configurations

Abreu,

Funk,

Krčadinac

et al. 2021

Preprint

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We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to the known families such as partial geometries and their generalizations or elliptic semiplanes are constructed. Necessary existence conditions are proved and a table of feasible parameters of such configurations with at most 200 points is presented. Non-existence of some configurations with feasible parameters is proved.

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“…This was generalised in [9] to strongly regular (α, β)-reguli giving rise to (α, β)-geometries with a strongly regular point graph. Here we will go one step further: we will introduce distance-regular (0, α)-reguli and obtain distance-regular geometries with α 3 = α.…”

mentioning

confidence: 99%

Distance-Regular (0,α)-Reguli

et al. 2006

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We introduce distance-regular (0, α)-reguli and show that they give rise to (0, α)-geometries with a distance-regular point graph. This generalises the SPG-reguli of Thas [14] and the strongly regular (α, β)-reguli of Hamilton and Mathon [9], which yield semipartial geometries and strongly regular (α, β)-geometries, respectively. We describe two infinite classes of examples, one of which is a generalisation of the well-known semipartial geometry T * n (B) arising from a Baer subspace PG(n, q) in PG(n, q 2 ).

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Strongly Regular (α, β)-Geometries

Cited by 8 publications

References 11 publications

Codes from strongly regular (α, β)-reguli

Codes from strongly regular (α, β)-reguli

Strongly regular configurations

Distance-Regular (0,α)-Reguli

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