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Coincident probabilities and applications in combinatorics

Published online by Cambridge University Press:  14 July 2016

Samuel Karlin
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Abstract

For a strong Markov process on the line with continuous paths the Karlin–McGregor determinant formula of coincidence probabilities for multiple particle systems is extended to allow the individual component processes to start at variable times and run for variable durations. The extended formula is applied to a variety of combinatorial problems including counts of non-crossing paths in the plane with variable start and end points, dominance orderings, numbers of dominated majorization orderings, and time-inhomogeneous random walks.

Keywords

NON-CROSSING PATHSDOMINANCE ORDERINGSMAJORIZATION
Type
Part 5 - Concepts of Coincidence and Convergence
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 185 - 200
Copyright
Copyright © Applied Probability Trust 1988 

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