Uwe Schwerdtfeger
Published 2012-08-07, updated 2012-08-13Version 2
We compute the limiting distribution of height of a random discrete excursion with step sets consisting of one positive step 1 and arbitrary finite set of non-positive integers. The limit law is the supremum of a Brownian excursion. This is well-known for Dyck and Motzkin paths. We apply a representation of the length and height generating function in terms of certain Schur polynomials put forward in a 2008 paper by Bousquet-Melout which leads to a form of the moment generating functions amenable to a Mellin transform analysis.
Comments: This paper has been withdrawn by the author due to an error in section 2.3. Unless a=1, more than the said k+1 tableaux have to be taken into account. As it stands the subsequent derivation is only valid for a=1, i.e. excursions with precisely one positive step 1 and an arbitrary finite set of non-positive steps
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