The minimum number of blocks in Pairwise Balanced Designs with maximum block size 4 : the final cases

Martin Grüttmüller; Ian T. Roberts; Sue D’Arcy; Judith Egan

doi:10.18453/rosdok_id00005834

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Martin Grüttmüller Ian T. Roberts Sue D’Arcy Judith Egan

The minimum number of blocks in Pairwise Balanced Designs with maximum block size 4 : the final cases

University of Rostock, Institute of Mathematics, 2005

https://doi.org/10.18453/rosdok_id00005834

Abstract: The minimum number of blocks having maximum size precisely four that are required to cover, exactly λ times, all pairs of elements from a set of cardinality v is denoted by gλ(4)(v) are known except for λ = 1 andv = 17 or 18. It is known that 30<= g(4)(17) <= 31 and 32 <= g(4)(18) <= 33. In this paper we Show that g(4)(17) =/ 30 and g(4)(18) =/ 32, thus finalising the Determination of gλ(4)(v) for all λ and v

Workingpaper Freier Zugang

Titel:

The minimum number of blocks in Pairwise Balanced Designs with maximum block size 4: the final cases

Schriftenreihe:

Preprints aus dem Institut für Mathematik, 05/13

Beteiligte Personen:

Martin Grüttmüller[VerfasserIn]
	122522559
Ian T. Roberts[VerfasserIn]
Sue D’Arcy[VerfasserIn]
Judith Egan[VerfasserIn]

Zusammenfassung:

The minimum number of blocks having maximum size precisely four that are required to cover, exactly λ times, all pairs of elements from a set of cardinality v is denoted by gλ(4)(v) are known except for λ = 1 andv = 17 or 18. It is known that 30<= g(4)(17) <= 31 and 32 <= g(4)(18) <= 33. In this paper we Show that g(4)(17) =/ 30 and g(4)(18) =/ 32, thus finalising the Determination of gλ(4)(v) for all λ and v [Englisch]

Dokumenttyp:

Workingpaper

Einrichtung:

Mathematisch-Naturwissenschaftliche Fakultät

Sprache:

Englisch

Sachgruppe der DNB:

510 Mathematik

Umfang:

1 Online-Ressource (12 Seiten)

Veröffentlichung /
Entstehung:

Rostock: University of Rostock, Institute of Mathematics