category: combinatorics [[combinatorics]] +-- {: .num_defn} ###### Definition Let $p$ be a prime number, let $n\in \mathbb{N}$. Then the *$n$-th $p$-adic Witt polynomial* is defined by $$w_n(X):=\sum_{d|n}d X_d^{n/d}$$ This formula comes out of consideration of addition of [[Teichmüller representatives]], a multiplicative section of the natural projection $A\to k$ of a discrete valuation ring to its [[residue field]]. This section is unique if $k$ is perfect. Witt polynomials are one way to define [[Witt vectors]]. ([Hazewinkel](#Hazewinkel)) =-- ## References * Hazewinkel, [Witt vectors](http://arxiv.org/abs/0804.3888).{#Hazewinkel}