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String pattern avoidance in generalized non-crossing trees

Abstract : 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 ̈oder paths.
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Yidong Sun, Zhiping Wang. String pattern avoidance in generalized non-crossing trees. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 11 (1), pp.79--93. ⟨hal-00988187⟩

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