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Colloquium on Trees in Algebra and Programming

CAAP 1996: Trees in Algebra and Programming — CAAP '96 pp 59–71Cite as

The area determined by underdiagonal lattice paths

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Part of the book series: Lecture Notes in Computer Science ((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.

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Authors and Affiliations

  1. Dipartimento di Sistemi e Informatica, via Lombroso 6/17, Firenze, Italy

    Donatella Merlini, Renzo Sprugnoli & M. Cecilia Verri

Authors
  1. Donatella Merlini
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  2. Renzo Sprugnoli
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  3. M. Cecilia Verri
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Editor information

Hélène Kirchner

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© 1996 Springer-Verlag Berlin Heidelberg

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Merlini, D., Sprugnoli, R., Verri, M.C. (1996). The area determined by underdiagonal lattice paths. In: Kirchner, H. (eds) Trees in Algebra and Programming — CAAP '96. CAAP 1996. Lecture Notes in Computer Science, vol 1059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61064-2_29

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  • DOI: https://doi.org/10.1007/3-540-61064-2_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61064-9

  • Online ISBN: 978-3-540-49944-2

  • eBook Packages: Springer Book Archive

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