doi:10.1016/j.jcta.2004.04.001
Copyright © 2004 Elsevier Inc. All rights reserved.
Asymptotics of combinatorial structures with large smallest component
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Edward A. Bender
, a, Atefeh Mashatan
, b, Daniel Panario
, c and L. Bruce Richmond
, b
a Department of Mathematics, University of California, San Diego, La Jolla 92093, USA
b Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada N2L 3G1
c School of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6
Received 5 May 2003.
Available online 18 May 2004.
Abstract
We study the probability of connectedness for structures of size n when all components must have size at least m. In the border between almost certain connectedness and almost certain disconnectedness, we encounter a generalized Buchstab function of n/m.
Author Keywords: Combinatorial enumeration; Components; Connectedness
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