#14574: Bender-Knuth involutions and standardization of semistandard Young
tableaux
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Reporter: darij | Owner:
sage-combinat
Type: enhancement | Status:
needs_review
Priority: major | Milestone: sage-5.10
Component: combinatorics | Resolution:
Keywords: tableaux, partitions, combinat | Work issues:
Report Upstream: N/A | Reviewers: Travis
Scrimshaw
Authors: Darij Grinberg | Merged in:
Dependencies: | Stopgaps:
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Comment (by darij):
Hi Travis! That was quick.
{{{skew_tableau.py}}}:
Oops, I have no idea how I managed to add a second {{to_row}} method
instead of changing the old one; thanks for being more attentive than I
was. But could you add these tests
{{{
sage: SkewTableau([[None, None, None],
[None]]).to_word_by_row()
word:
sage: SkewTableau([]).to_word_by_row()
word:
}}}
into the {{{to_word_by_row}}} method? Thanks. (Maybe also into
{{{to_word_by_column}}}?)
My reasoning behind the {{{straight=False}}} keyword is that when I call
standardization on a standard tableau, I don't want the output to be
checked for standardness twice (once for standardness as a skew standard
tableau, and then again for standardness when transformed into a standard
tableau). Is this a moot point? I am not sure if our classes actually do
all that checking, but even if they don't I assume they eventually will.
Here's something I should have done myself: In the docstring of
{{{to_permutation}}}, can you explain what "reading order" means? The
notation is not as standard as people think it is; for instance, van
Leeuwen's Littlewood-Richardson paper ( http://www-math.univ-
poitiers.fr/~maavl/pdf/lrr.pdf ) defines "a reading order" rather than
"the reading order". (And our reading order is neither Semitic nor Kanji;
I don't think anyone ever wrote in that order...)
On line 504 in your revision, replace "self" by "T".
On the next line, "revsersed" should be "reversed".
On line 515, "True" should be backticked from both sides.
Line 576 in your revision: "*Bender-Knuth involution*" should be "*`k`-th
Bender-Knuth involution*". Sorry, that one is my own oversight.
Line 587: "over all `i`" -> "over all `i` ranging over this iterable" (or
however this is normally said).
Line 591 of revision: Again, "True" needs more backticks.
Line 659: Why do you import {{{bisect_right}}} when you don't use it?
Lines 663-694: Is the compiler smart enough that replacing all those calls
of {{{result_tab[i]}}} by {{{result_tab_i}}} after first declaring
{{{result_tab_i}}} to be {{{result_tab[i]}}} won't add any performance? If
so, this could save me some work in the future.
Line 681: Add whitespaces to {{{k+1}}} for consistency.
{{{tableau.py}}}:
On the docstrings, most of the above stuff applies again (sorry for
duplication).
Line 885: Why the "skew"?
Line 892: why did you add "skew"?
Line 938: Could you pass the ``check`` variable as well? Or is this
automatic?
Line 939: Why Semistandard rather than Standard?
Good point that the theorems belong into the Examples, not the Tests
section. Good job on the docs as well.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14574#comment:6>
Sage <http://www.sagemath.org>
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