X/(1-q) Plethystic Substitution
Hello everyone!
I'm trying to perform the plethystic substitution f→f[X1−q] (which is given by f[X1−q]=f(x1,qx1,q2x1,...,x2,qx2,...))
I tried to implement this in Sage using the command .plethysm(X/(1-q)), but it doesn't seem to be giving me the right thing (I have no idea how it's interpreting 1/(1-q) actually). Does anyone know if this is implemented, and if so, how to get it to work?
Thanks so much in advance!
Ideally, provide enough code for others to reproduce what you did.
Hello Raymond! Long shot since I know this is years old, but did you ever figure out how to do this?
Edit: I figured it out! It's literally just f(X/(1-q)), assuming you've defined your f and X previously. So for me, "schur([3])(Z/(1-q))" returns exactly what Haiman says it should on page 46 of https://math.berkeley.edu/~mhaiman/ftp/newt-sf-2001/newt.pdf (https://math.berkeley.edu/~mhaiman/ft...) , given that I defined Z previously as p1, the powersum symmetric function for k = 1.