On the number of trees in Zd
- 21 June 1992
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 25 (12) , 3523-3528
- https://doi.org/10.1088/0305-4470/25/12/014
Abstract
The number of trees weakly embedded in the hypercubic lattice, tn, is considered. It is known that limn to infinity tn1n/= lambda 0, and that tn0n. These facts are proven by noting that trees satisfy a supermultiplicative inequality tntmn+m. A submultiplicative property is derived for trees of the form tn+m3 alpha log(n+m) tntm. Consequently, there exists a constant delta such that O(exp(- delta (logn)2) lambda 0nn0n.Keywords
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