Dipart. di Sistemi e Informatica

Universitá di Firenze, Firenze, Italy

elisa@dsi2.dsi.unifi.it

and

Boise State University, Boise, ID, U.S.A

sulanke@math.idbsu.edu

This paper considers combinatorial interpretations for two
triangular recurrence arrays containing
the Schröder numbers,
*s*_{n} = 1, 1, 3, 11, 45, 197, ...
and
*r*_{n} = 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.

**This is a source for sequences A001003, A006318, and A010683.**

**Temporary note: Currently a PostScript version of this paper can be
found on Sulanke's WEB page at
http://diamond.idbsu.edu/~sulanke/recentpapindex.html
**

- 1. Introduction
- 2. Schröder arrays and lattice paths
- 3. Zebras, generating trees and previous constructions
- 4. New constructions for zebras
- 5. A bijection between zebras and lattice paths
- 6. Generating function considerations
- 7. An algorithm for a product of zebras
- Bibliography