New lower bounds for t-coverings

Daniel Horsley; Rakhi Singh

doi:10.1002/jcd.21591

New lower bounds for t-coverings

Daniel Horsley, Rakhi Singh

School of Mathematics

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

2 Citations (Scopus)

Abstract

Fisher proved in 1940 that any 2- (v,k,λ) design with (Formula presented.) has at least v blocks. In 1975, Ray-Chaudhuri and Wilson generalized this result by showing that every t- (Formula presented.) design with (Formula presented.) has at least (Formula presented.) blocks. By combining methods used by Bose and Wilson in proofs of these results, we obtain new lower bounds on the size of t- (Formula presented.) coverings. Our results generalize lower bounds on the size of 2- (Formula presented.) coverings recently obtained by the first author.

Original language	English
Pages (from-to)	369-386
Number of pages	18
Journal	Journal of Combinatorial Designs
Volume	26
Issue number	8
DOIs	https://doi.org/10.1002/jcd.21591
Publication status	Published - 1 Aug 2018

Keywords

Fisher’s inequality
higher incidence matrix
t-covering

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10.1002/jcd.21591

Cite this

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AB - Fisher proved in 1940 that any 2- (v,k,λ) design with (Formula presented.) has at least v blocks. In 1975, Ray-Chaudhuri and Wilson generalized this result by showing that every t- (Formula presented.) design with (Formula presented.) has at least (Formula presented.) blocks. By combining methods used by Bose and Wilson in proofs of these results, we obtain new lower bounds on the size of t- (Formula presented.) coverings. Our results generalize lower bounds on the size of 2- (Formula presented.) coverings recently obtained by the first author.

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KW - higher incidence matrix

KW - t-covering

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New lower bounds for t-coverings

Abstract

Keywords

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Other files and links

Matchings in Combinatorial Structures

Partitioning and ordering Steiner triple systems

Cite this

New lower bounds for t-coverings

Abstract

Keywords

Access to Document

Other files and links

Projects

Matchings in Combinatorial Structures

Partitioning and ordering Steiner triple systems

Cite this