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Counting Pairs of Lattice Paths by Intersections

โœ Scribed by Ira Gessel; Wayne Goddard; Walter Shur; Herbert S. Wilf; Lily Yen

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
377 KB
Volume
74
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

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.

๐Ÿ“œ SIMILAR VOLUMES

Even and Odd Pairs of Lattice Paths with
Even and Odd Pairs of Lattice Paths with Multiple Intersections
โœ Ira M. Gessel; Walter Shur ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 345 KB

We study the numbers M n, k r, s , N n, r k =M n, k r, r , N E (n, k, p), and N O (n, k, p), prove several simple relations among them, and derive a simpler formula for M n, k r, s than appears in .

On Pairs of Lattice Paths with a Given N
On Pairs of Lattice Paths with a Given Number of Intersections
โœ Markus Fulmek ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 307 KB

This formula was proved in [2] by means of generating functions. ## 2. INTERPRETATION OF THE FORMULA'S SUMMANDS Our bijection is based on an appropriate lattice-path-interpretation for the formula's summands (pointed out by Krattenthaler [4]): Clearly, we article no. TA962754 154 0097-3165ร‚97 25.0