I looked around for some while but couldn't find anything. Is the pebbling number known for the grid $P_m\square P_n$? (I'm not asking about the optimal pebbling number.)
Pebbling number of the grid $P_m\square P_n$
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discrete-mathematics
graph-theory
reference-request
open-problem
1 Answers
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It is easy to see that $\pi(P_n \square P_m) \ge 2^{n + m - 2}$, because there is a case when all pebbles are placed in one corner and the root is in the opposite corner. On the other hand $2^{n + m - 2}$ pebbles should always be enough (this fact is neither completely obvious, nor too hard to see).