Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3

Gennian Ge; Martin Grüttmüller; Sven Hartmann; Rolf S. Rees

doi:10.18453/rosdok_id00005899

zum übergeordneten Dokument

Gennian Ge Martin Grüttmüller Sven Hartmann Rolf S. Rees

Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3

University of Rostock, Institute of Mathematics, 2005

https://doi.org/10.18453/rosdok_id00005899

Abstract: A mandatory representation design MRD(K;v) is a pairwise balanced design on v Points with block sizes from the set K in which for each k ∈ K there is at least one block in the design of size k. In this paper, we Show that the necessery criteria for an MRD(K;v) to exist are asymptotically sufficient for finite K. Furthermore, we consider MRDs with K = {4,k}, where k ≡ 2 mod 3, k ≥ 5. Here, we prove that the necessary conditions for existence are sufficient if v ≡ 2 mod 3 and v ≥ 18k^2, or v ≡ 0 mod 3 and v ≥ 12k^3, or v ≡ 1 mod 3 and v ≥ 8k^4.

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Titel:

Mandatory representation designs MRD(4, k; v) with k ≡ 2 mod 3

Schriftenreihe:

Preprints aus dem Institut für Mathematik, 05/2

Beteiligte Personen:

Gennian Ge[VerfasserIn]
Martin Grüttmüller[VerfasserIn]
	122522559
Sven Hartmann[VerfasserIn]
	118124978
Rolf S. Rees[VerfasserIn]
	122169727

Zusammenfassung:

A mandatory representation design MRD(K;v) is a pairwise balanced design on v Points with block sizes from the set K in which for each k ∈ K there is at least one block in the design of size k. In this paper, we Show that the necessery criteria for an MRD(K;v) to exist are asymptotically sufficient for finite K. Furthermore, we consider MRDs with K = {4,k}, where k ≡ 2 mod 3, k ≥ 5. Here, we prove that the necessary conditions for existence are sufficient if v ≡ 2 mod 3 and v ≥ 18k^2, or v ≡ 0 mod 3 and v ≥ 12k^3, or v ≡ 1 mod 3 and v ≥ 8k^4. [Englisch]

Dokumenttyp:

Workingpaper

Einrichtung:

Mathematisch-Naturwissenschaftliche Fakultät

Sprache:

Englisch

Sachgruppe der DNB:

510 Mathematik

Umfang:

1 Online-Ressource (22 Seiten)

Veröffentlichung /
Entstehung:

Rostock: University of Rostock, Institute of Mathematics