On an inclusion-exclusion formula based on the reflection principle
Discrete Mathematics
On lattice path counting by major index and descents
European Journal of Combinatorics
Reflection and algorithm proofs of some more Lie group dual pair identities
Journal of Combinatorial Theory Series A
Random Walks in Weyl Chambers and the Decomposition of Tensor Powers
Journal of Algebraic Combinatorics: An International Journal
q-Generalization of a ballot problem
Discrete Mathematics
Walks confined in a quadrant are not always D-finite
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Partially directed paths in a wedge
Journal of Combinatorial Theory Series A
A Kolmogorov-Smirnov Test for r Samples
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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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 technique to walks in the alcoves of the classical affine Weyl groups. In all cases, we get determinant formulas for the number of k-step walks. One important example is the region m x1 > x2 ... xn 0, which is a rescaled alcove of the affine Weyl group Cn. If each coordinate is considered to be an independent particle, this models n non-colliding random walks on the interval (0, m). Another case models n non-colliding random walks on a circle.