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Full-Text Articles in Algebra
A Survey Of Graphs Of Minimum Order With Given Automorphism Group, Jessica Alyse Woodruff
A Survey Of Graphs Of Minimum Order With Given Automorphism Group, Jessica Alyse Woodruff
Math Theses
We survey vertex minimal graphs with prescribed automorphism group. Whenever possible, we also investigate the construction of such minimal graphs, confirm minimality, and prove a given graph has the correct automorphism group.
Lattices From Hermitian Function Fields, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Lattices From Hermitian Function Fields, Albrecht Böttcher, Lenny Fukshansky, Stephan Ramon Garcia, Hiren Maharaj
Pomona Faculty Publications and Research
We consider the well-known Rosenbloom-Tsfasman function field lattices in the special case of Hermitian function fields. We show that in this case the resulting lattices are generated by their minimal vectors, provide an estimate on the total number of minimal vectors, and derive properties of the automorphism groups of these lattices. Our study continues previous investigations of lattices coming from elliptic curves and finite Abelian groups. The lattices we are faced with here are more subtle than those considered previously, and the proofs of the main results require the replacement of the existing linear algebra approaches by deep results of …
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
The Automorphism Group Of The Halved Cube, Benjamin B. Mackinnon
Theses and Dissertations
An n-dimensional halved cube is a graph whose vertices are the binary strings of length n, where two vertices are adjacent if and only if they differ in exactly two positions. It can be regarded as the graph whose vertex set is one partite set of the n-dimensional hypercube, with an edge joining vertices at hamming distance two. In this thesis we compute the automorphism groups of the halved cubes by embedding them in R n and realizing the automorphism group as a subgroup of GLn(R). As an application we show that a halved cube is a circulant graph if …