Regular Article
Counting Pairs of Lattice Paths by Intersections

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Abstract

We count the pairs of walks between diagonally opposite corners of a given lattice rectangle by the number of points in which they intersect. We note that the number of such pairs with one intersection is twice the number with no intersection and we give a bijective proof of that fact. Some probabilistic variants of the problem are also investigated.

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*

Supported by the National Science Foundation.

†

Supported by the Office of Naval Research.

‡

Supported by a Fellowship of the NSERC, Canada

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