Discrete Mathematics & Theoretical Computer Science, Vol 11, No 1 (2009)

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String Pattern Avoidance in Generalized Non-crossing Trees

Yidong Sun, Zhiping Wang


In this paper, the problem of string pattern avoidance in generalized non-crossing trees is studied. The generating functions for generalized non-crossing trees avoiding string patterns of length one and two are obtained. The Lagrange inversion formula is used to obtain the explicit formulas for some special cases. A bijection is also established between generalized non-crossing trees with special string pattern avoidance and little Schr\"{o}der paths.

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