Primitive one-factorizations and the geometry of mixed translations

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• 作者：A. Bonisoli ; S. Bonvicini
• 关键词：Live one-factorization ; Automorphism group ; Affine space
• 刊名：Discrete Mathematics
• 出版年：2008
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：28 March 2008
• 卷：308
• 期：5-6
• 页码：726-733
• 文件大小：173 K

摘要

We construct an infinite family of one-factorizations of one; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4PK8B6X-1&_mathId=mml1&_user=10&_cdi=5632&_rdoc=11&_acct=C000050221&_version=1&_userid=10&md5=fd5ce8780df96bb57bafdee0f0af9dd8" title="Click to view the MathML source">K_v admitting an automorphism group acting primitively on the set of vertices but no such group acting doubly transitively. We also give examples of one-factorizations which are live, in the sense that every one-factor induces an automorphism, but do not coincide with the affine line parallelism of one; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4PK8B6X-1&_mathId=mml2&_user=10&_cdi=5632&_rdoc=11&_acct=C000050221&_version=1&_userid=10&md5=da774e5986d1644b3737a44d697167ef" title="Click to view the MathML source">AG(n,2). To this purpose we develop the notion of a “mixed translation” in one; color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4PK8B6X-1&_mathId=mml3&_user=10&_cdi=5632&_rdoc=11&_acct=C000050221&_version=1&_userid=10&md5=c7fb0daf215d41fb71642fbd2ff0b5f4" title="Click to view the MathML source">AG(n,2).