Boolean Representations of Simplicial Complexes and Matroids
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classica
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John Rhodes Pedro V. Silva
Boolean Representations of Simplicial Complexes and Matroids
Springer Monographs in Mathematics
More information about this series at http://www.springer.com/series/3733
John Rhodes • Pedro V. Silva
Boolean Representations of Simplicial Complexes and Matroids
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John Rhodes Department of Mathematics University of California at Berkeley Berkeley, CA, USA
Pedro V. Silva Department of Mathematics University of Porto Porto, Portugal
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-319-15113-7 ISBN 978-3-319-15114-4 (eBook) DOI 10.1007/978-3-319-15114-4 Library of Congress Control Number: 2015931927 Mathematics Subject Classification (2010): 03E05, 03G10, 05-00, 05B25, 05B30, 05B35, 05D15, 05E45, 06-00, 06A11, 06A12, 06B15, 15B34, 16Y60, 51E14, 55P15, 55U10 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
In memory of Gian-Carlo Rota
Acknowledgments
Both the authors thank Anne Schilling, Benjamin Steinberg, James Oxley, and Stuart Margolis for their valuable comments. John Rhodes would like to thank his remarkable wife, Laura Morland, for all her love and support. Pedro V. Silva is grateful to his wife Margarida for her enduring support and for everything else! He also acknowledges support from • The European Regional Development Fund through the programme COMPETE and the Portuguese Government through FCT (Fundação para a Ciência e a Tecnologia) under the project PEst-C/MAT/UI0144/2013 • CNPq (Brazil) through a BJT-A grant (process 313768/2013-7)
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Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2
Boolean and Superboolean Matrices . . . . .
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