Give posets polynomials (order, characteristic, zeta, etc.)

[sagetrac-csar]

Adding some of the polynomials from Stembridge's Posets package for Maple (see http://www.math.lsa.umich.edu/~jrs/software/posetshelp.html), namely:

• characteristic polynomial (done)
• zeta polynomial (done)
• flag f-polynomial (done)
• flag h-polynomial (done)
• f-polynomial (done)
• h-polynomial (done)
• order polynomial (done)
• chain polynomial (done)
• W-polynomial
• antichain polynomial

apply:

• attachment: trac_13240-qfold.patch​
• attachment: trac_13240-review2-dg.patch

CC: @kevindilks

Component: combinatorics

Keywords: sd40, days45

Author: Alex Csar, Kevin Dilks, Frédéric Chapoton

Reviewer: Darij Grinberg, Nathann Cohen

Merged: sage-5.13.beta2

Issue created by migration from https://trac.sagemath.org/ticket/13240

[sagetrac-csar]

Changed keywords from sd40 to sd40, days45

[fchapoton]

comment:3

A first patch, with three of the simplest polynomials

[fchapoton]

comment:4

I have added the flag f-vector

[fchapoton]

comment:5

I have added the flag h-polynomial

[fchapoton]

comment:6

I have added the characteristic polynomial

[fchapoton]

Description changed:

--- 
+++ 
@@ -1,10 +1,10 @@
 Adding some of the polynomials from Stembridge's Posets package for Maple (see http://www.math.lsa.umich.edu/~jrs/software/posetshelp.html), namely:
 
-* characteristic polynomial
-* W-polynomial
-* zeta polynomial
-* flag f-polynomial
-* flag h-polynomial
-* f-polynomial
-* h-polynomial
+* characteristic polynomial (done)
+* W-polynomial 
+* zeta polynomial (done)
+* flag f-polynomial (done)
+* flag h-polynomial (done)
+* f-polynomial (done)
+* h-polynomial (done)
 * order polynomial

[sagetrac-csar]

comment:8

I think we have code from Sage Days 45 for the order polynomial (which is one line once you have zeta), the antichain polynomial and the chain polynomial.

[fchapoton]

comment:9

great ! could you post it here as a patch on top of mine ?

[sagetrac-csar]

comment:10

Will do. I'm compiling sage at the moment, but I should be able to do it sometime this evening (GMT -6).

Note several hours later: compiling took way longer than expected. Will add to the patch tomorrow.