Document Type

Article

Publication Date

2007

Publication Title

Journal of Integer Sequences

Abstract

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.

Volume

10

First Page

1

Last Page

34

ISSN

1530-7638

Comments

This is a pre-publication version of an article published in Journal of Integer Sequences. The final authenticated version is available online at: https://cs.uwaterloo.ca/journals/JIS/VOL10/Roberts/wildpart2.html

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