The number of t-wise balanced designs

Charles J. Colbourn; Dean G. Hoffman; Kevin T. Phelps; Vojtěch Rödl; Peter M. Winkler

doi:10.1007/BF01205073

The number of t-wise balanced designs

Charles J. Colbourn, Dean G. Hoffman, Kevin T. Phelps, Vojtěch Rödl, Peter M. Winkler

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We prove that the number of t-wise balanced designs of order n is asymptotically {Mathematical expression}, provided that blocks of size t are permitted. In the process, we prove that the number of t-profiles (multisets of block sizes) is bounded below by {Mathematical expression} and above by {Mathematical expression} for constants c₂>c₁>0.

Original language	English (US)
Pages (from-to)	207-218
Number of pages	12
Journal	Combinatorica
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/BF01205073
State	Published - Sep 1 1991
Externally published	Yes

Keywords

AMS subject classification (1980): 05B30, 05B05

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/BF01205073

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abstract = "We prove that the number of t-wise balanced designs of order n is asymptotically {Mathematical expression}, provided that blocks of size t are permitted. In the process, we prove that the number of t-profiles (multisets of block sizes) is bounded below by {Mathematical expression} and above by {Mathematical expression} for constants c2>c1>0.",

keywords = "AMS subject classification (1980): 05B30, 05B05",

author = "Colbourn, {Charles J.} and Hoffman, {Dean G.} and Phelps, {Kevin T.} and Vojt{\v e}ch R{\"o}dl and Winkler, {Peter M.}",

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AU - Colbourn, Charles J.

AU - Hoffman, Dean G.

AU - Phelps, Kevin T.

AU - Rödl, Vojtěch

AU - Winkler, Peter M.

PY - 1991/9/1

Y1 - 1991/9/1

N2 - We prove that the number of t-wise balanced designs of order n is asymptotically {Mathematical expression}, provided that blocks of size t are permitted. In the process, we prove that the number of t-profiles (multisets of block sizes) is bounded below by {Mathematical expression} and above by {Mathematical expression} for constants c2>c1>0.

AB - We prove that the number of t-wise balanced designs of order n is asymptotically {Mathematical expression}, provided that blocks of size t are permitted. In the process, we prove that the number of t-profiles (multisets of block sizes) is bounded below by {Mathematical expression} and above by {Mathematical expression} for constants c2>c1>0.

KW - AMS subject classification (1980): 05B30, 05B05

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U2 - 10.1007/BF01205073

DO - 10.1007/BF01205073

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SP - 207

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JO - Combinatorica

JF - Combinatorica

IS - 3

ER -

The number of t-wise balanced designs

Abstract

Keywords

ASJC Scopus subject areas

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