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On the Number of Unary-Binary Tree-Like Structures with Restrictions on the Unary Height
Verfasser / Verfasserin Bodini, Olivier ; Gardy, Daniele ; Gittenberger, Bernhard ; Golebiewski, Zbigniew
Erschienen in
Annals of Combinatorics, 2018, Jg. 22, H. 1, S. 45-91
ErschienenSpringer Nature, 2018
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (EN)asymptotic enumeration / generating functions / lambda-terms / trees / directed acyclic graphs / nested square-roots / singularity analysis
ISSN0218-0006
URNurn:nbn:at:at-ubtuw:3-5026 Persistent Identifier (URN)
DOI10.1007/s00026-018-0371-7 
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On the Number of Unary-Binary Tree-Like Structures with Restrictions on the Unary Height [1.93 mb]
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Zusammenfassung (Englisch)

We investigate various classes of Motzkin trees as well as lambda-terms for which we derive asymptotic enumeration results. These classes are defined through various restrictions concerning the unary nodes or abstractions, respectively: we either bound their number or the allowed levels of nesting. The enumeration is done by means of a generating function approach and singularity analysis. The generating functions are composed of nested square roots and exhibit unexpected phenomena in some of the cases. Furthermore, we present some observations obtained from generating such terms randomly and explain why usually powerful tools for random generation, such as Boltzmann samplers, face serious difficulties in generating lambda-terms.

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CC-BY-Lizenz (4.0)Creative Commons Namensnennung 4.0 International Lizenz