scholarly journals Double-coset enumeration algorithm for symmetrically generated groups

2005 ◽  
Vol 2005 (5) ◽  
pp. 699-715 ◽  
Author(s):  
Mohamed Sayed
Keyword(s):  
Double Coset ◽  
Computer Implementation ◽  
Enumeration Algorithm ◽  
Coset Enumeration

A double-coset enumeration algorithm for groups generated by symmetric sets of involutions together with its computer implementation is described.

scholarly journals On semigroup presentations

1993 ◽  
Vol 36 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Edmund F. Robertson ◽  
Yusuf Ünlü
Keyword(s):  
Group Presentation ◽  
Enumeration Algorithm ◽  
Long Period ◽  
Coset Enumeration ◽  
Finitely Presented

Semigroup presentations have been studied over a long period, usually as a means of providing examples of semigroups. In 1967 B. H. Neumann introduced an enumeration method for finitely presented semigroups analogous to the Todd–Coxeter coset enumeration process for groups. A proof of Neumann's enumeration method was given by Jura in 1978.In Section 3 of this paper we describe a machine implementation of a semigroup enumeration algorithm based on that of Neumann. In Section 2 we examine certain semigroup presentations, motivated by the fact that the corresponding group presentation has yielded interesting groups. The theorems, although proved algebraically, were suggested by the semigroup enumeration program.

scholarly journals Double coset enumeration

1991 ◽  
Vol 12 (4-5) ◽  
pp. 415-426 ◽  
Author(s):  
Stephen A. Linton
Keyword(s):  
Double Coset ◽  
Coset Enumeration

10.—Applications of the Todd-Coxeter Algorithm to Generalised Fibonacci Groups

1975 ◽  
Vol 73 ◽  
pp. 163-166 ◽  
Author(s):  
C. M. Campbell ◽  
E. F. Robertson
Keyword(s):  
Enumeration Algorithm ◽  
Coset Enumeration

SynopsisWe use programmes for the Todd-Coxeter coset enumeration algorithm and the modified Todd-Coxeter coset enumeration algorithm to investigate a class of generalised Fibonacci groups. In particular we use these techniques to discover a finite non-metacyclic Fibonacci group and to study its structure.

Double coset enumeration of symmetrically generated groups

2004 ◽  
Vol 7 (2) ◽  
Author(s):  
John N. Bray ◽  
Robert T. Curtis
Keyword(s):  
Double Coset ◽  
Coset Enumeration

scholarly journals On a Group Presentation Due to Fox

1976 ◽  
Vol 19 (2) ◽  
pp. 247-248 ◽  
Author(s):  
C. M. Campbell ◽  
E. F. Robertson
Keyword(s):  
General Problem ◽  
Direct Proof ◽  
Fundamental Groups ◽  
Algebraic Proof ◽  
Group Presentation ◽  
Enumeration Algorithm ◽  
Coset Enumeration

In 1956 R. H. Fox had occasion, while investigating fundamental groups of topological surfaces, to believe that the group <a, b | ab2=b3a, ba2=a2b> was trivial. Using the Todd-Coxeter coset enumeration algorithm a proof was obtained, see [3], and this algorithmic proof was used to produce an algebraic proof, see [2]. In [1] Benson and Mendelsohn, using a similar method to that of [2] showed that <a, b | abn=bn+1a, ban=an+1b> is trivial. In this note we give a direct proof for the more general problem of describing the structure of the group <a, b | abn=bℓa, ban=aℓb>.

scholarly journals A note on the Todd-Coxeter coset enumeration algorithm

1976 ◽  
Vol 20 (1) ◽  
pp. 73-79 ◽  
Author(s):  
M. J. Beetham ◽  
C. M. Campbell
Keyword(s):  
Finite Index ◽  
Finitely Generated ◽  
Enumeration Algorithm ◽  
Finitely Presented Group ◽  
Coset Enumeration ◽  
The Given ◽  
Finitely Presented

In (8) Todd and Coxeter described an algorithm for enumerating the cosets of a finitely generated subgroup of finite index in a finitely presented group. Several authors ((1), (2), (5), (6), (7)) have discussed a modification of the algorithm to give also a presentation of the subgroup in terms of the given generators.

Efficient computer implementation to test the validity of the generalized version of Chargaff’s second parity rule.

2016 ◽  
Author(s):  
Gonzalo Riadi ◽  
Camilo Fuentes ◽  
Karen Orostica ◽  
Eduardo Alarcón ◽  
Ignacio Vidal
Keyword(s):  
Computer Implementation ◽  
Parity Rule

The Location Problem of Given and Indivisible Different Units

1970 ◽  
Vol 2 (3) ◽  
pp. 341-356
Author(s):  
G. Jándy
Keyword(s):  
Exact Solution ◽  
Heuristic Algorithm ◽  
Network Flow ◽  
Location Problem ◽  
Optimal Solution ◽  
Type Problem ◽  
Distribution Problem ◽  
Enumeration Algorithm ◽  
Weighted Distribution ◽  
Partial Enumeration

In cases where certain simplifications are allowed, the location optimisation of given and indivisible different economic units may be modelled as a bi-value weighted distribution problem. The paper presents a heuristic algorithm for this network-flow-type problem and also a partial enumeration algorithm for deriving the exact solution. But it is also pointed out that an initial sub-optimal solution can quickly be improved with a derivation on a direct line only, if the exact solution is not absolutely essential. A numerical example is used to illustrate the method of derivation on a direct line starting with an upper bound given by a sub-optimal solution.

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