Searching for authors named "George Havas" – sorted by Relevance.
17 documents found, showing 1 through 10.
Next 10 →
-
Andrews-Curtis And Todd-Coxeter Proof Words
- …Andrews and Curtis have conjectured that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. It can be difficult to determine whether or not the conjecture holds for a particular presentation. We show th…
- Cited by 2 (1 self) – Add To MetaCart
-
Experiments in Coset Enumeration
- …. Coset enumeration, based on the methods described by Todd and Coxeter, is one of the most important tools for investigating finitely presented groups. Such methods do not, in general, constitute an algorithm. Each problem has to be addressed individually, and determining whether or not an acce…
- Cited by 7 (6 self) – Add To MetaCart
-
Proving a Group Trivial Made Easy: A Case Study in Coset Enumeration
- …: Coset enumeration, based on the methods described by Todd and Coxeter, is one of the basic tools for investigating finitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems.…
- Cited by 3 (2 self) – Add To MetaCart
-
Parallel Coset Enumeration Using Threads
- …Introduction Coset enumeration is long established as a technique for the investigation of finitely presented groups. It takes a finitely presented group and a finitely presented subgroup as input, and attempts to find the index of the subgroup in the whole group. Various detailed accounts 2;4;7;9…
- Cited by 1 (1 self) – Add To MetaCart
-
Breadth-first search and the Andrews-Curtis conjecture
- …Andrews and Curtis have conjectured that every balanced presentation of the trivial group can be transformed into the standard presentation by a finite sequence of elementary transformations. Previous computational work on this problem has been based on genetic algorithms. We show that a computation…
- Cited by 3 (0 self) – Add To MetaCart
-
The Trivial Group Made Easy: A Case Study in Coset Enumeration
- …: Coset enumeration, based on the methods described by Todd & Coxeter, is one of the basic tools for investigating finitely presented groups. The process is not well understood, and various pathological presentations of, for example, the trivial group have been suggested as challenge problems. H…
- Cited by 2 (1 self) – Add To MetaCart
-
A New Algorithm and Refined Bounds for Extended Gcd Computation
- …. Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipl…
- Cited by 4 (2 self) – Add To MetaCart
-
4-Engel groups are locally nilpotent
- …Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.…
- Cited by 2 (1 self) – Add To MetaCart
-
On Routing In Circulant Graphs
- …We investigate various problems related to circulant graphs -- finding the shortest path between two vertices, finding the shortest loop, and computing the diameter. These problems are related to shortest vector problems in a special class of lattices. We give matching upper and lower bounds on the …
- Cited by 2 (1 self) – Add To MetaCart
-
Trades and Defining Sets: Theoretical and Computational Results
- …Given a particular combinatorial structure, there may be many distinct objects having this structure. When investigating these, two natural questions to ask are: . Given two objects, where and how do they differ? . How much of an individual object is necessary to uniquely identify it? These two q…
- Cited by 1 (0 self) – Add To MetaCart
Showing 1 through 10.
Next 10 →
