X/(1-q) Plethystic Substitution

asked 2021-04-06 08:07:49 +0100

RaymondChou gravatar image

Hello everyone!

I'm trying to perform the plethystic substitution $f \rightarrow f[\frac{X}{1-q}]$ (which is given by $ f[\frac{X}{1-q}] = f(x_1,qx_1,q^2x_1,...,x_2,qx_2,...)$)

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!

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Comments

1

Ideally, provide enough code for others to reproduce what you did.

slelievre gravatar imageslelievre ( 2021-04-06 10:17:51 +0100 )edit

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.

Keith Sullivan gravatar imageKeith Sullivan ( 2024-11-11 17:43:11 +0100 )edit