Schr�der Triangles, Paths, and Parallelogram Polyominoes
Elisa Pergola
Dipart. di Sistemi e Informatica
Universit� di Firenze, Firenze, Italy
Email address: [email protected]
and
Robert A. Sulanke
Boise State University, Boise, ID, U.S.A
Email address: [email protected]
Abstract:
This paper considers combinatorial interpretations for two
triangular recurrence arrays containing
the Schr�der numbers
sn = 1, 1, 3, 11, 45, 197, ...
and
rn = 1, 2, 6, 22, 90, 394, ... , for
n = 0, 1, 2, ....
These interpretations involve the
enumeration of constrained lattice paths and bicolored
parallelogram polyominoes,
called zebras.
In addition to two recent inductive constructions of zebras and their associated
generating trees, we present two new ones and a bijection between zebras and
constrained lattice paths.
We use the constructions with generating
function methods to count sets of zebras
with respect to natural parameters.
�
Received Apr. 21 1998 and in revised form May 23 1998. Published in Journal of Integer Sequences May 29, 1998.
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