## Ars Combinatoria, Volumes 5-6Department of Combinatorics and Optimization, University of Waterloo., 1978 - Combinatorial analysis |

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### Contents

Some Constructions for KReconstruction | 3 |

Linear Orderings Satisfying Certain Constraints | 19 |

Parallelism of Stelner Quadruple Systems | 27 |

Copyright | |

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### Common terms and phrases

1-factorization adjacent algorithm association scheme assume automorphism base trees cell collection Combinatorial Theory complete graph component conjecture consider construction contains COROLLARY cyclic triples decomposition define definition denote design of type digram disconnected graphs disjoint circles double cover double cover hypergraph edges elements embedded exactly example exists factor finite function given graph G Graph Theory Hadamard matrices hence implies integer intersection involution IP(q Jennifer Seberry Lehmer LEMMA Let G matrix of order mutually orthogonal latin n-BD-graph obtained orthogonal designs orthogonal latin squares pair parameters partial parallel classes partially balanced partition permutation positive integer primality testing prime power prove quasigroups reconstruct reconstruction conjecture resolvable quadruple system result ro ro ro ro Ul satisfying SPBIBD squares of order Steiner triple systems strongly regular graph subsets Suppose symbols system of order triple systems Ul Ul Ul vertex vertices Waterloo