Generalized Schröder Numbers and the Rotation Principle
Universiteit van die Vrystaat
Departement van Wiskunde
Given a point-lattice
, we determine the number of
royal paths from
with unit steps
, which never go below the line
, by means of the
rotation principle. Compared to the method of "penetrating
analysis'', this principle has here the advantage of greater clarity
and enables us to find meaningful additive decompositions of
Schröder numbers. It also enables us to establish a connection to
coordination numbers and the crystal ball in the cubic lattice
. As a by-product we derive a recursion for the number
of North-East turns of rectangular lattice paths and construct a
WZ-pair involving coordination numbers and Delannoy numbers.
Full version: pdf,
(Concerned with sequences
Received January 8 2007;
revised version received May 8 2007; July 25 2007.
Published in Journal of Integer Sequences, July 25 2007.
Journal of Integer Sequences home page