Clarendon Press, 1999 - 560 pàgines
Among the simplest combinatorial designs, triple systems are a natural generalization of graphs and have connections with geometry, algebra, group theory, finite fields, and cyclotomy. Applications of triple systems are found in coding theory, cryptography, computer science, and statistics. In
many cases, triple systems provide the prototype for deep results in combinatorial design theory, and a number of important results were first understood in the context of triple systems and then generalized. This book attempts to survey current knowledge on the subject, to gather together common
themes, and to provide an accurate portrait of the huge variety of problems and results. It includes representative samples of the major styles of proof technique and a comprehensive bibliography.
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An historical introduction
Isomorphism and invariants
Subsystems and holes
Large sets and partitions
STSs with two subsystems
Nested and derived triple systems
1-factorization 3-GDD of type addition admits algorithm appears apply automorphism bound choose Colbourn collection colour complete configurations conjecture consider construction contains covering cycle cyclic define designs determine difference direct disjoint distinct edges elements embedding employ establish exactly examine example exists extension fixed follows four given gives graph hence hole integer intersection isomorphism Kirkman large set latin square least leave Lemma length Math maximum Mendelsohn method modulo multigraph multiplier multiset necessary neighbourhood obtain occurs orbit pair parallel classes partial triple system partition points possible prime problem produce Proof prove quasigroup remaining repeated result Rosa simple sizes solution Steiner triple systems STS(u STS(v subsystem sufficient Suppose symbols system of order Table Theorem Theory treat triangles TS(v vertex vertices Write