ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 30 May 2013 09:18:37 +0200Plethysym as composition of functionshttps://ask.sagemath.org/question/10165/plethysym-as-composition-of-functions/On [this page](http://www.sagemath.org/doc/reference/combinat/sage/combinat/sf/sf.html#sage.combinat.sf.sf.SymmetricFunctions) the `plethysym` function is described as "composition of functions". Is this implying that writing
`s[2](s[lambda])` for some other partition $\lambda$ is like taking the symmetric square of the schur function corresponding to $\lambda$?Wed, 29 May 2013 18:03:57 +0200https://ask.sagemath.org/question/10165/plethysym-as-composition-of-functions/Answer by niles for <p>On <a href="http://www.sagemath.org/doc/reference/combinat/sage/combinat/sf/sf.html#sage.combinat.sf.sf.SymmetricFunctions">this page</a> the <code>plethysym</code> function is described as "composition of functions". Is this implying that writing
<code>s[2](s[lambda])</code> for some other partition $\lambda$ is like taking the symmetric square of the schur function corresponding to $\lambda$?</p>
https://ask.sagemath.org/question/10165/plethysym-as-composition-of-functions/?answer=14989#post-id-14989I don't know the answer to this question, but you may be able to determine it yourself by looking at the source code for `plethysm`. You can do this with `.plethysm??`, as in
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: s2 = s[2]
sage: s2.plethysm??
Also (I apologize if you've already checked this) the Wikipedia page on plethysm is very short, but includes a cryptic comment which may help you decide if your guess is correct or not. Good luck!
Thu, 30 May 2013 09:18:37 +0200https://ask.sagemath.org/question/10165/plethysym-as-composition-of-functions/?answer=14989#post-id-14989