  We examine the non-symmetric Macdonald polynomials $E_\lambda(x;q,t)$ at
$q=1$, as well as the more general permuted-basement Macdonald polynomials.
When $q=1$, we show that $E_\lambda(x;1,t)$ is symmetric and independent of $t$
whenever $\lambda$ is a partition. Furthermore, we show that for general
$\lambda$, this expression factors into a symmetric and a non-symmetric part,
where the symmetric part is independent of $t$, while the non-symmetric part
only depends on the relative order of the entries in $\lambda$.
  We also examine the case $q=0$, which give rise to so called
permuted-basement $t$-atoms. We prove expansion-properties of these, and as a
corollary, prove that Demazure characters (key polynomials) expand positively
into permuted-basement atoms. This complements the result that
permuted-basement atoms are atom-positive. Finally, we show that a product of a
permuted-basement atom and a Schur polynomial is again positive in the same
permuted-basement atom basis, and thus interpolates between two results by
Haglund, Luoto, Mason and van Willigenburg.
  The common theme in this project is the application of basement-permuting
operators as well as combinatorics on fillings, by applying results in a
previous article by the first author.
