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The area determined by underdiagonal lattice paths

  • Donatella Merlini
  • Renzo Sprugnoli
  • M. Cecilia Verri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1059)

Abstract

We use the “first passage decomposition” methodology to study the area between various kinds of underdiagonal lattice paths and the main diagonal. This area is important because it is connected to the number of inversions in permutations and to the internal path length in various types of trees. We obtain the generating functions for the total area of all the lattice paths from the origin to the point (n, n). Since this method also determines the number of these paths, we are able to obtain exact results for the average area.

Keywords

underdiagonal lattice paths average area first passage decomposition generating functions context-free grammars 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Donatella Merlini
    • 1
  • Renzo Sprugnoli
    • 1
  • M. Cecilia Verri
    • 1
  1. 1.Dipartimento di Sistemi e InformaticaFirenzeItaly

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