String Pattern Avoidance in Generalized Non-crossing Trees
Yidong Sun, Zhiping Wang
Abstract
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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