Opened 6 years ago

Closed 6 years ago

# Delete yamanouchi.py

Reported by: Owned by: darij minor sage-5.13 combinatorics yamanouchi, dyck words, littlewood-richardson, combinat, days54 sage-combinat, aschilling, nthiery, darij sage-5.13.beta3 Jeroen Demeyer Travis Scrimshaw N/A

Here is the whole content of sage/combinat/yamanouchi.py:

r"""
Yamanouchi Words

A right (respectively left) Yamanouchi word on a completely ordered
alphabet, for instance [1,2,...,n], is a word math such that any
right (respectively left) factor of math contains more entries math
than math. For example, the word [2, 3, 2, 2, 1, 3, 1, 2, 1, 1] is
a right Yamanouchi one.

The evaluation of a word math encodes the number of occurrences of
each letter of math. In the case of Yamanouchi words, the
evaluation is a partition. For example, the word [2, 3, 2, 2, 1, 3,
1, 2, 1, 1] has evaluation [4, 4, 2].

Yamanouchi words can be useful in the computation of
Littlewood-Richardson coefficients c_{\lambda, \mu}^\nu.
According to the Littlewood-Richardson
rule, c_{\lambda, \mu}^\nu is the number of skew tableaux
of shape \nu / \lambda and evaluation \mu,
whose row readings are Yamanouchi words.
"""


(added by #1685 but no code was ever written for that file)

The "math" looks like the text has been copypasted from some website; this is embarassing...

### comment:1 Changed 6 years ago by darij

• Description modified (diff)

### comment:2 Changed 6 years ago by jdemeyer

• Authors set to Jeroen Demeyer
• Description modified (diff)
• Status changed from new to needs_review
• Summary changed from yamanouchi.py: what is it for? to Delete yamanouchi.py

### comment:3 follow-up: ↓ 5 Changed 6 years ago by tscrim

• Cc aschilling nthiery darij added

It looks like it was added in #1685 with no content, as if it was going to have code to be used in computing LR coefficients. I'm tempted to remove it as there currently is no code, but it would be nice to have a simple generator for all Yamanouchi words.

Nicolas, Anne, Darij, do any of you currently have code to generate Yamanouci words (without appealing to the crystals code)? I have an idea about how to do it and could whip something up in a few hours if you think it's worthwhile to have.

### comment:4 Changed 6 years ago by darij

I guess the algorithm outlined in the last paragraph of p. 7 of http://wwwmathlabo.univ-poitiers.fr/~maavl/pdf/lrr.pdf (except that \nu, I guess, should be taken to be a tableau formed by n pairwise incomparable cells) should do the trick. I have never implemented such a thing and am not currently planning to; I can very well imagine it being useful (along with the general algorithm for generating companion tableaux -- or is this already done in crystals code?).

### comment:5 in reply to: ↑ 3 Changed 6 years ago by aschilling

Nicolas, Anne, Darij, do any of you currently have code to generate Yamanouci words (without appealing to the crystals code)? I have an idea about how to do it and could whip something up in a few hours if you think it's worthwhile to have.

I am currently in the process of finishing a paper with Jennifer on Yamanouchi elements for flag Gromov-Witten invariants. These are natural generalizations of the usual Littlewood-Richardson rules. But I think this code (which at k->infity would be the usual LR coefficients) would be more natural in the crystal environment. In terms of crystals Yamanouchi elements are just highest weight elements. So in principle I do not mind removing this file (or next week we could add them from the crystal set-up).

Best,

Anne