More nonexistence results for symmetric pair coverings

Francetic, Nevena, Herke, Sarada and Horsley, Daniel (2015) More nonexistence results for symmetric pair coverings. Linear Algebra and Its Applications, 487 43-73. doi:10.1016/j.laa.2015.09.006


Author Francetic, Nevena
Herke, Sarada
Horsley, Daniel
Title More nonexistence results for symmetric pair coverings
Journal name Linear Algebra and Its Applications   Check publisher's open access policy
ISSN 0024-3795
1873-1856
Publication date 2015-12-15
Sub-type Article (original research)
DOI 10.1016/j.laa.2015.09.006
Open Access Status Not Open Access
Volume 487
Start page 43
End page 73
Total pages 31
Place of publication Philadelphia, PA, United States
Publisher Elsevier
Language eng
Subject 2602 Algebra and Number Theory
2607 Discrete Mathematics and Combinatorics
2608 Geometry and Topology
2612 Numerical Analysis
Formatted abstract
A (v,k,λ)-covering is a pair (V,B), where V is a v-set of points and B is a collection of k-subsets of V (called blocks), such that every unordered pair of points in V is contained in at least λ blocks in B. The excess of such a covering is the multigraph on vertex set V in which the edge between vertices x and y has multiplicity rxy - λ, where rxy is the number of blocks which contain the pair {x,y}. A covering is symmetric if it has the same number of blocks as points. Bryant et al. [4] adapted the determinant related arguments used in the proof of the Bruck-Ryser-Chowla Theorem to establish the nonexistence of certain symmetric coverings with 2-regular excesses. Here, we adapt the arguments related to rational congruence of matrices and show that they imply the nonexistence of some cyclic symmetric coverings and of various symmetric coverings with specified excesses.
Keyword Almost difference set
Bruck-Ryser-Chowla Theorem
Excess
Hasse-Minkowski invariant
Pair covering
Rationally congruent matrices
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Non HERDC
 
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