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Almost all Steiner triple systems are almost resolvable

Part of: Spectral theory and eigenvalue problems Calculus on manifolds; nonlinear operators Classical differential geometry

Published online by Cambridge University Press:  03 November 2020

Asaf Ferber  and
Matthew Kwan
Asaf Ferber
Affiliation:
Department of Mathematics, University of California, Irvine, California, USA; E-mail: asaff@uci.edu
Matthew Kwan
Affiliation:
Department of Mathematics, Stanford University, Stanford, California94305,USA; E-mail: mattkwan@stanford.edu

Abstract

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We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).

Keywords

survey designmeasurement errormachine learning

MSC classification

Primary: 35P15: Estimation of eigenvalues, upper and lower bounds
Secondary: 58C40: Spectral theory; eigenvalue problems 53A07: Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
Type
Discrete Mathematics
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e39
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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