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Let n particles move in standard Brownian motion in one dimension, with the process terminating if two particles collide. This is a speciic case of Brownian motion constrained to stay inside a Weyl… (More)

We consider a class of random walks introduced by Gessel and Zeilberger for which the reflection principle can be used to count the number of k-step walks between two points on a lattice (typically… (More)

- David J. Grabiner
- J. Comb. Theory, Ser. A
- 2002

Abstract. We use a reflection argument, introduced by Gessel and Zeilberger, to count the number of k-step walks between two points which stay within a chamber of a Weyl group. We apply this… (More)

- David J. Grabiner
- Electr. J. Comb.
- 2006

Let μ be a partition of k, and T a standard Young tableau of shape μ. McKay, Morse, and Wilf show that the probability a randomly chosen Young tableau of N cells contains T as a subtableau is… (More)

This paper describes the cutting sequences of geodesic flow on the modular surface H/PSL(2, Z) with respect to the standard fundamental domain F = {z = x + iy : −2 ≤ x ≤ 12 and |z| ≥ 1} of PSL(2, Z).… (More)

A partition of the positive integers into sets A and B avoids a set S ⊂ N if no two distinct elements in the same part have a sum in S. If the partition is unique, S is uniquely avoidable. For any… (More)

- David J. Grabiner
- Discrete Mathematics
- 1999

- David J. Grabiner
- J. Comb. Theory, Ser. A
- 1995

The m m determinant of hyperbolic Bessel functions det jI a i ?b j (2x)j can be factored into two smaller determinants by elementary operations if a i = ?a m+1?i and b i = ?b m+1?i. We give… (More)