Generating functions for bi-wall directed polygons (CROSBI ID 578476)
Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Feretić, Svjetlan
engleski
Generating functions for bi-wall directed polygons
Directed animals have two fairly large subsets for which generating functions are known. Those two subsets are called column-convex directed polygons and diagonally convex directed polygons ; each of them has an algebraic perimeter generating function satisfying a cubic equation. The area generating function of column-convex directed polygons is a rational function, while the area generating function of diagonally convex directed polygons is a q-series. In this paper, we introduce a new model, called bi-wall directed polygons. The definition of a bi-wall directed polygon requires that, when the boundary of the figure is traversed clockwise (starting from the lower left corner), after the first leftward step there are no more upward steps. Bi-wall directed polygons are a subset of directed animals and a superset both of column-convex directed polygons and of diagonally convex directed polygons. Bi-wall directed polygons have an algebraic perimeter generating function (which satisfies a quadratic equation) and a rational area generating function.
bi-wall directed polygons; enumeration; perimeter generating function; quadratic equation; area generating function; rational; left Motzkin factors
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Podaci o prilogu
147-151.
2010.
objavljeno
Podaci o matičnoj publikaciji
Lattice Path Combinatorics and Applications, Siena, 4-7 th July 2010
Mohanty, Sri Gopal ; Rinaldi, Simone
Siena: Dipartimento di Scienze Matematiche e Informatiche
Podaci o skupu
The Seventh International Conference on Lattice Path Combinatorics and Applications
predavanje
04.07.2010-07.07.2010
Siena, Italija