Directed and multi-directed animals on the King's lattice

Axel Bacher (1, 2, 3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 LIPN - Laboratoire d'Informatique de Paris-Nord

We define the directed King's lattice to be the square lattice with diagonal (next nearest neighbor) bonds and with the preferred directions {←,↖,↑,↗,→}. We enumerate directed animals on this lattice using a bijection with Viennot's heaps of pieces. We also define and enumerate a superclass of directed animals, the elements of which are called multi-directed animals. This follows Bousquet-Mélou and Rechnitzer's work on the directed triangular and square lattices. Our final results show that directed and multi-directed animals asymptotically behave similarly to the ones on the triangular and square lattices.

Domaines: Combinatoire [math.CO]

Axel Bacher. Directed and multi-directed animals on the King's lattice. EuroComb 2013, Sep 2013, Pise, Italy. pp 535-541, ⟨10.1007/978-88-7642-475-5_84⟩. ⟨hal-00989608⟩