Patterns in treeshelves |
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Authors: | Jean-Luc Baril Sergey Kirgizov Vincent Vajnovszki |
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Institution: | LE2I CNRS, Université Bourgogne Franche-Comté, 21078 Dijon, France |
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Abstract: | We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.) The considered patterns are sub-treeshelves, and for each such a pattern we provide exponential generating function for the corresponding distribution and popularity. Finally, we present constructive bijections between treeshelves avoiding a pattern of size three and some classes of simpler combinatorial objects. |
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Keywords: | Binary increasing tree Pattern Statistic Popularity Bell/Euler(ian)/Lah number |
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