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  • 标题:Counting Ascents in Generalized Dyck Paths
  • 作者:Benjamin Hackl ; Clemens Heuberger ; Helmut Prodinger
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:110
  • 页码:26:1-26:15
  • DOI:10.4230/LIPIcs.AofA.2018.26
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:Non-negative Lukasiewicz paths are special two-dimensional lattice paths never passing below their starting altitude which have only one single special type of down step. They are well-known and -studied combinatorial objects, in particular due to their bijective relation to trees with given node degrees. We study the asymptotic behavior of the number of ascents (i.e., the number of maximal sequences of consecutive up steps) of given length for classical subfamilies of general non-negative Lukasiewicz paths: those with arbitrary ending altitude, those ending on their starting altitude, and a variation thereof. Our results include precise asymptotic expansions for the expected number of such ascents as well as for the corresponding variance.
  • 关键词:Lattice path; Lukasiewicz path; ascent; asymptotic analysis; implicit function; singular inversion
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