Coincident probabilities and applications in combinatorics
- 1 January 1988
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 25 (A) , 185-200
- https://doi.org/10.2307/3214156
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
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