Bijective Recurrences concerning Schro"der Paths

@article{Sulanke1998BijectiveRC,
  title={Bijective Recurrences concerning Schro"der Paths},
  author={Robert A. Sulanke},
  journal={Electr. J. Comb.},
  year={1998},
  volume={5}
}
Consider lattice paths in Z2 with three step types: the up diagonal (1, 1), the down diagonal (1,−1), and the double horizontal (2, 0). For n ≥ 1, let Sn denote the set of such paths running from (0, 0) to (2n, 0) and remaining strictly above the x-axis except initially and terminally. It is well known that the cardinalities, rn = |Sn|, are the large Schröder numbers. We use lattice paths to interpret bijectively the recurrence (n+ 1)rn+1 = 3(2n− 1)rn− (n− 2)rn−1, for n ≥ 2, with r1 = 1 and r2… CONTINUE READING
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