Recursive enumeration of clusters in general dimension on hypercubic lattices

A recursive method for enumerating clusters on a hypercubic lattice in d spatial dimensions is presented from which the weak embedding constants are determined as polynomials in d. A tabulation for all clusters having no free ends is available for $n_b$≤15, where $n_b$ is the number of bonds. As illustrated here and elsewhere, this tabulation can be used to generate many series expansions. A novel method of checking the enumeration with an algebraic calculation is presented.