Abstract
We derive asymptotics for the moments of the height distribution of watermelons with $p$ branches with wall. This generalises a famous result by de Bruijn, Knuth and Rice on the average height of planted plane trees, and a result by Fulmek on the average height of watermelons with two branches.
Highlights
The model of vicious walkers was introduced by Fisher [4]
The model of vicious walkers is concerned with p random walkers on a d-dimensional lattice
A configuration that attracted much interest amongst mathematical physicists and combinatorialists is the watermelon configuration, which is a special case of the two dimensional vicious walker model
Summary
The height of watermelons with wall - Extended Abstract. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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