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The theorem of Gutman et al. (1983) is applied to calculate the number of spanning trees in the carbon-carbon connectivity-network of the recently diagnosed C,,cluster buckminsterfullerene. This "complexity" turns out to be approximately 3.75 x lozo and it is found necessary to invoke the device of modulo arithmetic and the "Chinese Remainder Theorem" in order to evaluate it precisely on a small computer. The exact spanningtree count for buckminsterfullerene is 375 291 866 372 898 816 000, or, ZZ5 X 34 X 53 X 115 X 19'. A "ringcurrent" calculation by the method of McWeeny may be based on any desired one of this vast number of spanning trees.

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A partition on a nonempty set 5 is a collection of disjoint nonempty subsets, called blocks, whose union is S. The recursion formula 2Z.1 (n-1\ (1) B» = T,(.)Bi (n^l,B0=l) for the number of partitions on a finite set with n elements is well known (cf. Rota [4]). We obtain equation (2) which generalizes (1) and which yields a derivation of the Möbius function for partition lattices different from those in [2], [3] and [5]. Let S be a finite nonempty set. Two partitions a and it of 5 satisfy a^ir if every block of

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