136 research outputs found
Some Implications on Amorphic Association Schemes
AMS classifications: 05E30, 05B20;amorphic association scheme;strongly regular graph;(negative) Latin square type;cyclotomic association scheme;strongly regular decomposition
Uniformity in Association schemes and Coherent Configurations: Cometric Q-Antipodal Schemes and Linked Systems
2010 Mathematics Subject Classification. Primary 05E30, Secondary 05B25, 05C50, 51E12
Jordan-Holder theorem for imprimitivity systems and maximal decompositions of rational functions
In this paper we prove several results about the lattice of imprimitivity
systems of a permutation group containing a cyclic subgroup with at most two
orbits. As an application we generalize the first Ritt theorem about functional
decompositions of polynomials, and some other related results. Besides, we
discuss examples of rational functions, related to finite subgroups of the
automorphism group of the sphere for which the first Ritt theorem fails to be
true.Comment: In the current version the approach was considerably simplified and a
lot of new material was added (see e.g. Section 2.2, Section 2.3 and Section
3.2). On the other hand, some results of rather calculating character were
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Some Implications on Amorphic Association Schemes
AMS classifications: 05E30, 05B20;
The Cayley isomorphism property for Cayley maps
The Cayley Isomorphism property for combinatorial objects was introduced by L. Babai in 1977. Since then it has been intensively studied for binary relational structures: graphs, digraphs, colored graphs etc. In this paper we study this prop- erty for oriented Cayley maps. A Cayley map is a Cayley graph provided by a cyclic rotation of its connection set. If the underlying graph is connected, then the map is an embedding of a Cayley graph into an oriented surface with the same cyclic rotation around every vertex. Two Cayley maps are called Cayley isomorphic if there exists a map isomorphism between them which is a group isomorphism too. We say that a finite group H is a CIM-group1 if any two Cayley maps over H are isomorphic if and only if they are Cayley isomorphic. The paper contains two main results regarding CIM-groups. The first one provides necessary conditons for being a CIM-group. It shows that a CIM-group should be one of the following ā¤m Ć ā¤r 2, ā¤m Ć ā¤4, ā¤m Ć ā¤8, ā¤m Ć Q8, ā¤m ā ā¤2e, e = 1, 2, 3, where m is an odd square-free number and r a non-negative integer2. Our second main result shows that the groups ā¤m Ć ā¤r 2, ā¤m Ć ā¤4, ā¤m Ć Q8 contained in the above list are indeed CIM-groups. Ā© 2018, Australian National University. All rights reserved
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