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Consecutive Pattern Avoidances in Non-crossing Trees

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Abstract

In this paper, motivated by the concepts of increasing (alternating) non-crossing trees, the problem of consecutive pattern avoidances in non-crossing trees is proposed. Some given patterns of length two and three are investigated in detail. The Lagrange inversion formula is used to obtain the explicit formulas for these cases. Bijections are established between non-crossing trees avoiding special patterns and Schröder paths.

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Authors and Affiliations

  1. Department of Mathematics, Dalian Maritime University, 116026, Dalian, People’s Republic of China

    Yidong Sun & Zhiping Wang

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  1. Yidong Sun
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  2. Zhiping Wang
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Correspondence to Yidong Sun.

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Sun, Y., Wang, Z. Consecutive Pattern Avoidances in Non-crossing Trees. Graphs and Combinatorics 26, 815–832 (2010). https://doi.org/10.1007/s00373-010-0950-9

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  • DOI: https://doi.org/10.1007/s00373-010-0950-9

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