Lattice Path Combinatorics and Applications

Recent methods used in lattice path combinatorics and various related branches of enumerative combinatorics are grouped together and presented in this volume, together with relevant applications. Contributions are mainly comprised of research articles tho

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George E. Andrews Christian Krattenthaler Alan Krinik Editors

Lattice Path Combinatorics and Applications

Developments in Mathematics Volume 58

Series editors Krishnaswami Alladi, Gainesville, FL, USA Pham Huu Tiep, Department of Mathematics, Rutgers University, Piscataway, NJ, USA Loring W. Tu, Department of Mathematics, Tufts University, Medford, MA, USA

The Developments in Mathematics (DEVM) book series is devoted to publishing well-written monographs within the broad spectrum of pure and applied mathematics. Ideally, each book should be self-contained and fairly comprehensive in treating a particular subject. Topics in the forefront of mathematical research that present new results and/or a unique and engaging approach with a potential relationship to other fields are most welcome. High quality edited volumes conveying current state-of-the-art research will occasionally also be considered for publication. The DEVM series appeals to a variety of audiences including researchers, postdocs, and advanced graduate students.

More information about this series at http://www.springer.com/series/5834

George E. Andrews Christian Krattenthaler Alan Krinik •



Editors

Lattice Path Combinatorics and Applications

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Editors George E. Andrews Department of Mathematics The Pennsylvania State University University Park, PA, USA

Christian Krattenthaler Fakultät für Mathematik Universität Wien Vienna, Austria

Alan Krinik Department of Mathematics and Statistics California State Polytechnic University, Pomona Pomona, CA, USA

ISSN 1389-2177 ISSN 2197-795X (electronic) Developments in Mathematics ISBN 978-3-030-11101-4 ISBN 978-3-030-11102-1 (eBook) https://doi.org/10.1007/978-3-030-11102-1 Library of Congress Control Number: 2018966396 © Springer Nature Switzerland AG 2019 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. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the re