Journal of Integer Sequences
We introduce the notion of wild partition to describe in combinatorial language an important situation in the theory of p-adic fields. For Q a power of p, we get a sequence of numbers λQ,n counting the number of certain wild partitions of n. We give an explicit formula for the corresponding generating function ΛQ(x) = ΣλQ,nxn and use it to show that λ1/n Q,n tends to Q1/(p-1). We apply this asymptotic result to support a finiteness conjecture about number fields. Our finiteness conjecture contrasts sharply with known results for function fields, and our arguments explain this contrast.
David P. Roberts. Wild Partitions and Number Theory. Journal of Integer Sequences 10 (2007), Article 07.6.6.