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Combinatorial Mathematics VIII pp 293–303Cite as

Deques, trees and lattice paths

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 884))

Abstract

A double ended queue or deque is a linear list for which all insertions and deletions occur at the ends of the list. We give a direct, ‘pictorial’ proof of a result of Knuth on the enumeration of permutations obtainable from output restricted deques. This approach readily identifies the numbers of these permutations as Schröder numbers and leads naturally to correspondences with other equinumerous sets of trees and lattice paths. We also gather together other references to occurrences of the Schröder numbers.

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Author information

Authors and Affiliations

  1. 68, Liverpool Road, WD18DN, Watford, Herts., England

    D. G. Rogers & L. W. Shapiro

  2. Mathematics Department, Howard University, 20059, Washington, D.C., USA

    D. G. Rogers & L. W. Shapiro

Authors
  1. D. G. Rogers
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  2. L. W. Shapiro
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Kevin L. McAvaney

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© 1981 Springer-Verlag

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Rogers, D.G., Shapiro, L.W. (1981). Deques, trees and lattice paths. In: McAvaney, K.L. (eds) Combinatorial Mathematics VIII. Lecture Notes in Mathematics, vol 884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091826

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  • DOI: https://doi.org/10.1007/BFb0091826

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  • Print ISBN: 978-3-540-10883-2

  • Online ISBN: 978-3-540-38792-3

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