Sheik Ahmed Ullah

Consequence of Schreier-Sims Algorithm in Solving Rubik¿s Cube

Base, Orbit, Strong generating Set, Schreier Structure are explored and programmed through GAP coding

• Broschiertes Buch

Produktbeschreibung

Successful computation with a permutation group is largely depended on our ability to find an effective representative for the group. In particular many calculations can be facilitated if we have a coset representative for each subgroup of the chain in its predecessor. So we have tried in this book to construct a chain in which each subgroup is a point stabilizer of the last. These concepts were introduced by Schrier-Sims as an effective description of a permutation group. For the holistic idea we have described various versions of the Schreier-Sims Algorithm. Finally in solving Rubik s Cube, we have thoroughly discussed the structure and various subgroups of Rubik s Cube before applying the Schreier-Sims Algorithm. These subgroups are easier to understand and solve. We have marked the 48 moving squares to convert the twists of Rubik s Cube in to permutation cycle. Handling an enormous group like the Rubik s Cube Group becomes very easy when we use the Schreier-Sims Algorithm to form the stabilizer chain of the Rubik s Cube Group. This stabilizer chain was then used to factorize a random element of the Rubik s Cube Group, which will lead us to the solution of the Rubik's Cube.

Produktdetails

• Verlag: LAP Lambert Academic Publishing
• Aufl.
• Seitenzahl: 100
• Erscheinungstermin: 2. Juli 2012
• Englisch
• Abmessung: 220mm x 150mm x 6mm
• Gewicht: 168g
• ISBN-13: 9783659150784
• ISBN-10: 3659150789
• Artikelnr.: 36075815

Autorenporträt

Mr. Sheik Ahmed Ullah has obtained his Master's Degree in Pure Mathematics in 2010 from the University of Dhaka, Bangladesh. Since then He is working as a Lecturer in Mathematics at BRAC University, Bangladesh. He is a co-author of an article published in a reputed journal and a book published in an international academic publishing.