| RANDOM WALK IN A WEYL CHAMBER 1 (2008) | |||||||||||||||
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| Abstract: The classical Ballot problem that counts the number of ways of walking from the origin and staying within the wedge x1 ≥ x2 ≥... ≥ xn (which is a Weyl chamber for the symmetric group), using positive unit steps, is generalized to general Weyl groups and general sets of steps. To any simple and natural proof, one can ask the question: How far can it be generalized? We will attempt to give one possible answer to this question for Andre”s[A] celebrated solution of the two-candidate ballot problem. Andre’s proof uses a reflection argument, and we will show that it can be naturally generalized to the context of Coxeter-Weyl ([Co], [H], [H1], [BG]) general finite | |||||||||||||||
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