Gaps in samples of geometric random variables

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225-239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at (http://www.ulb.ac.be/di/mcs/louchard/) (number 81 on the list) or at (http://math.sun.ac.za/similar to prodinger/pdffiles/gapsAPRIL27.pdf.) In particular, since the notion of a gap differs in these two papers, we derive some of the results obtained in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at (http://www.ulb.ac.be/di/mcs/louchard/) (number 81 on the list) or at (http://math.sun.ac.za/similar to prodinger/Pdffiles/gapsAPRIL27.pdf.)] for gaps as defined in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225-239]. (C) 2007 Elsevier B.V. All rights reserved.