Napredna pretraga

Generating functions for bi-wall directed polygons

Feretić, Svjetlan
Generating functions for bi-wall directed polygons // Lattice Path Combinatorics and Applications, Siena, 4-7 th July 2010 / Mohanty, Sri Gopal ; Rinaldi, Simone (ur.).
Siena, Italija: Dipartimento di Scienze Matematiche e Informatiche, 2010. str. 147-151 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)

Naslov
Generating functions for bi-wall directed polygons

Autori
Feretić, Svjetlan

Izvornik
Lattice Path Combinatorics and Applications, Siena, 4-7 th July 2010 / Mohanty, Sri Gopal ; Rinaldi, Simone - Siena, Italija : Dipartimento di Scienze Matematiche e Informatiche, 2010, 147-151

Skup
The Seventh International Conference on Lattice Path Combinatorics and Applications

Mjesto i datum
Siena, Italija, 04-07.07.2010

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Bi-wall directed polygons; enumeration; perimeter generating function; quadratic equation; area generating function; rational; left Motzkin factors

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika