Published online by Cambridge University Press: 05 May 2010
The aim of this monograph is to give a comprehensive and up-to-date presentation of the theory of finite linear spaces. For the most part, we take a combinatorial approach to the subject, but in the final chapter group theory is introduced.
The text is designed as a research resource for those working in the area of finite linear spaces, while the structure of the book also encourages its use as a graduate level text. At the end of each chapter, there is a section of exercises designed to test and extend a student's knowledge of the material in that chapter. There is also a research problem section containing current open problems which can be tackled with the aim of producing a thesis or a journal publication.
In the first chapter, constructions of affine and projective spaces are reviewed, and the fundamental results on finite linear spaces are given. Chapters 2 through 6 cover the work done on the major problem areas in linear spaces taking the ‘planar’ view: classification of linear spaces with given parameters, embeddability of linear spaces in “suitably small” projective planes. In Chapter 7 we consider problems of embedding higher dimensional linear spaces in projective spaces. Finally, in Chapter 8, assumptions are introduced on the collineation groups of linear spaces, and the recent results on characterization are presented.
There are several people we wish to thank for their assistance, encouragement and patience while this book was being written.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.