Implement the Murnaghan-Nakayama formula for character values of symmetric groups

[amritanshu-prasad]

The Murnaghan-Nakayama formula is a recursive formula for a character value of the symmetric group (for the statement, look at the second paragraph of Mark Wildon's answer http://mathoverflow.net/a/134620/9672 on mathoverflow, or Theorem 2.4.7 in Representation Theory of the Symmetric Group by James and Kerber).

CC: @tscrim @darijgr @sagetrac-sage-combinat @KPanComputes

Component: combinatorics

Keywords: partitions, character

Author: Keren Shao

Branch/Commit: public/mnRules @ 04d133d

Issue created by migration from https://trac.sagemath.org/ticket/15555

[amritanshu-prasad]

Changed keywords from partitions to partitions, days60

[SmartestKen]

Branch: public/mnRules

[SmartestKen]

Commit: 04d133d

[SmartestKen]

Changed keywords from partitions, days60 to partitions, character

[SmartestKen]

New commits:

04d133d

murnaghan nakayama rule under Partition

[SmartestKen]

Author: Keren Shao

[dimpase]

comment:6

a couple of quick comments:

the 1st line of the docstring should be separated from the rest by an empty line, i.e.
not

+        r"""
+        Return `\chi^{\lambda/\mu}(\alpha)` value in Murnaghan-Nakayama formula
+        (Enumerative Combinatorics (Stanley) equation 7.75)
...

but

+        r"""
+        Return `\chi^{\lambda/\mu}(\alpha)` value in Murnaghan-Nakayama formula
+
+        (Enumerative Combinatorics (Stanley) equation 7.75)
...

The reference should be made properly (by the way, which volume it is , I guess vol. 2?)
we already have it, so just use [EnumComb2]_

---

I am not sure that the recursive function should be public, and not an internal function in the non-recursive one. Also, the debugging flag should be a function parameter (default value False)

[tscrim]

comment:8

Some additional comments:

I don't see the point of making these static methods attached to Partition. That is not the natural place I would look for them. Furthermore, get_chi is a very non-descriptive name and needs to be changed. Actually, these might best as a normal method attached to SkewPartition (with a redirect in Partition with the skew being the empty partition).

I agree with Dima that the get_chi_recursive should not be public since it is essentially an internal function.

The ALGORITHM: block is over-indented (this is because it only (as it should) has one colon).

Do not return None if there is a check failure; raise an error message as intended.

Why are the keys for refDict strings and not the data as a tuple?

Please follow Python naming conventions (lower_case variable names). Also, try to avoid the extra blanklines.

[SmartestKen]

comment:9

Thanks for the comment.

Working on all issues Dima and tscrim mentioned. I have a few questions though.

1. Are all the docstring rules the same for internal function? (i.e. Do I just copy/paste the entire docstring for the current get_chi_recursive())?
2. The reason why I use static is
   i. it seems unnatural to call something like lda.get_chi(mu, alpha). And user will have to make Partition Object first before they can call the function.
   iii. I do not rely on any methods from Partition/Skewed-Partition Object and I cannot figure out how to extract the underlying list from a Partition Object (.get_part() does not look like a nice option...)
3. By redirecting, you mean on the docstring or make a redirect in function call? Please teach me how to do if you mean docstring.

[dimpase]

comment:10

by the way, did you look at @CachedFunction decorator, which provides memoization, so you don't need to carry around refDict at all?

this would make the code cleaner, and you could roll the two functions, recursive and non-recursive, into one.

[embray]

comment:11

Ticket retargeted after milestone closed

[mkoeppe]

comment:12

Batch modifying tickets that will likely not be ready for 9.1, based on a review of the ticket title, branch/review status, and last modification date.

[mkoeppe]

comment:14

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[mkoeppe]

comment:15

Setting a new milestone for this ticket based on a cursory review.