Maximal spanning time for neighborhood growth on the Hamming plane
نویسنده
چکیده
We consider a long-range growth dynamics on the two-dimensional integer lattice, initialized by a finite set of occupied points. Subsequently, a site x becomes occupied if the pair consisting of the counts of occupied sites along the entire horizontal and vertical lines through x lies outside a fixed Young diagram Z. We study the extremal quantity μ(Z), the maximal finite time at which the lattice is fully occupied. We give an upper bound on μ(Z) that is linear in the area of the bounding rectangle of Z, and a lower bound √ s− 1, where s is the side length of the largest square contained in Z. We give more precise results for a restricted family of initial sets, and for a simplified version of the dynamics.
منابع مشابه
Neighborhood Growth Dynamics on the Hamming Plane
We initiate the study of general neighborhood growth dynamics on two-dimensional Hamming graphs. The decision to add a point is made by counting the currently occupied points on the horizontal and the vertical line through it, and checking whether the pair of counts lies outside a fixed Young diagram. We focus on two related extremal quantities. The first is the size of the smallest set that ev...
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