Schröder Triangles, Paths, and Parallelogram Polyominoes
Elisa Pergola
Dipart. di Sistemi e Informatica
Universitá di Firenze, Firenze, Italy
Email address: elisa@dsi2.dsi.unifi.it
and
Robert A. Sulanke
Boise State University, Boise, ID, U.S.A
Email address: sulanke@math.idbsu.edu
Abstract:
This paper considers combinatorial interpretations for two
triangular recurrence arrays containing
the Schröder 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 April 21 1998; revised, May 23 1998. Published in
Journal of Integer Sequences, May 29 1998.
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