In this paper, we study some properties of Whitney numbers of Dowling lattices and related polynomials. We answer the following question: there is a relation between Stirling and Eulerian polynomials. Can we find a new relation between Dowling polynomials and other polynomials generalizing Eulerian polynomials? In addition, some congruences for the Dowling numbers are given. Mathematics Subject...

Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view Dowling lattices and new results about line-closed geometries. We complement these topics by showing that line-closure gives simple geometric proofs of the (mostly known) basic results about Dowling lattices. We pursue the topic of line-clo...

We show that the projective geometry PG(r − 1, q) for r > 3 is the only rank-r (combinatorial) geometry with (qr − 1)/(q − 1) points in which all lines have at least q + 1 points. For r = 3, these numerical invariants do not distinguish between projective planes of the same order, but they do distinguish projective planes from other rank-3 geometries. We give similar characterizations of affine...

A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data Parkinson's disease and parkinsonism in the elderly / edited by Jolyon Meara and William C. Koller. p. ; cm. Includes bibliographical references and index. Every effort has been made in preparing this book to provide accurate and up-to-date information which is in accord wi...