Abstract
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.
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Bacher, A. (2013). Directed and multi-directed animals on the King’s lattice. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_84
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DOI: https://doi.org/10.1007/978-88-7642-475-5_84
Publisher Name: Edizioni della Normale, Pisa
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