Filtering the coefficients of the \([2^k]\)-series for Brown-Peterson homology (Q1580298)

Let BP be the Brown-Peterson spectrum at the prime \(2\) and let \(\mu(X,Y)\) be its formal group law. For non-negative integers \(k\), the \([2^{k}]\)-series is inductively defined by \[ \left[2^{k+1}\right](T)= \mu\left(\left[2^{k}\right](T),\left[2^{k}\right](T)\right), \] with \(\left[2^{0}\right](T) = T\). The \([2^{k}]\)-series takes the form \[ [2^{k}](T) = \sum_{s \geq 0} a_{k,s}T^{s+1} \] where \(a_{k,s} \in \text{BP}_{*} = Z_{(2)}[v_{1}, v_{2}, \ldots ]\) has dimension \(2s\). This paper identifies \(k\) monomials that appear in \(a_{k,s}\).