  We present combinatorial rules (one theorem and two conjectures) concerning
three bases of Z[x1,x2,....]. First, we prove a "splitting" rule for the basis
of key polynomials [Demazure '74], thereby establishing a new positivity
theorem about them. Second, we introduce an extension of [Kohnert '90]'s
"moves" to conjecture the first combinatorial rule for a certain deformation
[Lascoux '01] of the key polynomials. Third, we use the same extension to
conjecture a new rule for the Grothendieck polynomials [Lascoux-Schutzenberger
'82].
