Designs
This chapter introduces the topic of finite combinatorial designs. The defining parameters of the designs are determined and their restrictions are proved. Special attention is given to Steiner triple systems, nets, and biplanes.
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Steven T. Dougherty
Combinatorics and Finite Geometry
Springer Undergraduate Mathematics Series Advisory Editors Mark A. J. Chaplain, St. Andrews, UK Angus Macintyre, Edinburgh, UK Simon Scott, London, UK Nicole Snashall, Leicester, UK Endre Süli, Oxford, UK Michael R. Tehranchi, Cambridge, UK John F. Toland, Bath, UK
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Steven T. Dougherty
Combinatorics and Finite Geometry
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Steven T. Dougherty Department of Mathematics University of Scranton Scranton, PA, USA
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-030-56394-3 ISBN 978-3-030-56395-0 (eBook) https://doi.org/10.1007/978-3-030-56395-0 Mathematics Subject Classification: 05, 06, 51, 52, 94 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
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Preface
The mathematics that will be discussed in this text falls into the branch of mathematics known as combinatorics. Combinatorics is a very old and very large branc
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