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- Walter Shur, Walter Shur
- 2017

- Ira M. Gessel, Wayne Goddard, Walter Shur, Herbert S. Wilf, Lily Yen
- J. Comb. Theory, Ser. A
- 1996

Consider an r × (n − r) plane lattice rectangle, and walks that begin at the origin (south-west corner), proceed with unit steps in either of the directions east or north, and terminate at the north-east corner of the rectangle. For each integer k we ask for N k , the number of ordered pairs of these walks that intersect in exactly k points. The number of… (More)

- Walter Shur
- 2004

Two players compete in a contest where the first player to win a specified number of points wins the game, and the first player to win a specified number of games wins the set. This paper proves two generalized inequalities, each independent of the probability of winning a point, concerning the better player’s chances of winning. Counterexamples are given… (More)

1. The algorithm. Huang [1] gives an algorithm for computing the powers of a triangular matrix where the diagonal elements are unique. However, in contrast to Huang’s algorithm, the method presented here has the unique advantage of producing the result in closed form, which shows explicitly how the behavior of any element of the matrix varies with varying… (More)

- Walter Shur
- Electr. J. Comb.
- 1997

- Ira M. Gessel, Walter Shur
- J. Comb. Theory, Ser. A
- 1996

Let be the number of ordered pairs of paths in the plane, with unit steps E or N, that intersect k times in which the first path ends at the point (r,n-r) and the second path ends at the point (s,n-s). Let and We study the numbers , , , and , prove several simple relations among them, and derive a simpler formula for than appears in [1].

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