On 3/30/11 6:06 AM, Martin Rubey wrote:
Anne Schilling writes:
sage: t = Tableau([[1,1,3],[2,3]])
sage: L = LinearExtension((t, 2))
sage: L.promotion()
[[1,1,2],[2,3]]
Usual semistandard tableaux are already defined on a totally ordered
alphabet {1,2,...,n+1}. So in this case, it would not a
Hi Dan, Nicolas, Jean, Jason, Martin, ...
This is now implemented. I also added a section on the Lusztig involution
to the thematic tutorial. Everything is posted on trac and the sage-combinat
server. Hopefully this is now close to being finished!
Best,
Anne
On 3/29/11 11:51 PM, Nicola
> the thematic tutorial.
>
> Since this method should eventually be moved to root systems (if not
> in DynkinDiagram!), I would not advertise it at this point. Or did you
> mean doc about the Sch�tzenberger involution?
I meant the Schutzenberger and Lusztig involutions.
Dan
--
You received th
Anne Schilling writes:
>> sage: t = Tableau([[1,1,3],[2,3]])
>> sage: L = LinearExtension((t, 2))
>> sage: L.promotion()
>> [[1,1,2],[2,3]]
>
> Usual semistandard tableaux are already defined on a totally ordered
> alphabet {1,2,...,n+1}. So in this case, it would not add much.
Yes, it only give
Hi Martin,
On 3/30/11 2:04 AM, Martin Rubey wrote:
Martin Rubey writes:
"Nicolas M. Thiery" writes:
As for posets, I don't know. I would tend to first write a draft of
the method in Posets, and then decide if the interfaces and
implementations are similar enough to be shared or not.
Here
Martin Rubey writes:
> "Nicolas M. Thiery" writes:
>
>> As for posets, I don't know. I would tend to first write a draft of
>> the method in Posets, and then decide if the interfaces and
>> implementations are similar enough to be shared or not.
>
> Here goes:
> # http://www.combinatorics.org/V
Hi Anne, Dan, Jean,
> Jean:
> the opposition automorphism
Thanks Jean! It's great to have experts with many different points of
view around :-)
On Tue, Mar 29, 2011 at 06:56:05PM -0700, bump wrote:
> I was going to suggest making it a method of ClassicalCrystals (so
> it would be availab
Anne wrote:
> The standard name in the literature for the automorphism (which may be
> trivial)
> induced by -w0 is
> "the opposition automorphism"
This seems better to me.
I was going to suggest making it a method of ClassicalCrystals (so it
would be
available for other crystals besides crysta
On 3/29/11 9:15 AM, Jean MICHEL wrote:
On Tue, Mar 29, 2011 at 08:16:53AM -0700, Daniel Bump wrote:
When the Dynkin diagram has a nontrivial automorphism (of order
two except D4), the map alpha -> -w0(alpha) may or not
coincide with this automorphism.
...
Here there is a non-trivial graph aut
On Tue, Mar 29, 2011 at 08:16:53AM -0700, Daniel Bump wrote:
> When the Dynkin diagram has a nontrivial automorphism (of order
> two except D4), the map alpha -> -w0(alpha) may or not
> coincide with this automorphism.
...
> Here there is a non-trivial graph automorphism but this
> isn't it. Theref
> sage: T.dynkin_diagram_automorphism_w0()
When the Dynkin diagram has a nontrivial automorphism (of order
two except D4), the map alpha -> -w0(alpha) may or not
coincide with this automorphism.
The issue is with type D_n.
If n is odd, then alpha -> -w0(alpha) is a nontrivial permutation
Hi Nicolas,
Ok, I changed this from an attribute to a cached method with doc string
and doc tests. I agree that this could live in root system, but for the
moment I kept this in the crystal code.
Best,
Anne
On 3/29/11 12:45 AM, Nicolas M. Thiery wrote:
Hi Anne,
On Mon, Mar 28
Hi Anne,
On Mon, Mar 28, 2011 at 03:55:19PM -0700, Anne Schilling wrote:
> On 3/28/11 3:21 PM, Daniel Bump wrote:
> >
> >The patch contains this:
> >
> >ind = lambda i: (-w0.action(alpha[i])).support()[0]
> >
> >This would be called for each element of hw, which
> >depends on the distance
On 3/28/11 3:21 PM, Daniel Bump wrote:
The patch contains this:
ind = lambda i: (-w0.action(alpha[i])).support()[0]
This would be called for each element of hw, which
depends on the distance to the highest weight vector.
That's not so bad, but if you looped over the crystal and
computed the in
The patch contains this:
ind = lambda i: (-w0.action(alpha[i])).support()[0]
This would be called for each element of hw, which
depends on the distance to the highest weight vector.
That's not so bad, but if you looped over the crystal and
computed the involution for every element, it would be
c
On 3/28/11 6:41 AM, Anne Schilling wrote:
On 3/28/11 6:28 AM, bump wrote:
Yes, it also exists for any Cartan type, but my impression was that then
it is called Lusztig involution. My plan is indeed to eventually implement
the Lusztig involution in CrystalOfTableauxElements. What do you think?
"Nicolas M. Thiery" writes:
> As for posets, I don't know. I would tend to first write a draft of
> the method in Posets, and then decide if the interfaces and
> implementations are similar enough to be shared or not.
Here goes:
# http://www.combinatorics.org/Volume_16/PDF/v16i2r9.pdf
# Figure
On 3/28/11 6:28 AM, bump wrote:
Yes, it also exists for any Cartan type, but my impression was that then
it is called Lusztig involution. My plan is indeed to eventually implement
the Lusztig involution in CrystalOfTableauxElements. What do you think?
That sounds like the right approach. Actual
> Yes, it also exists for any Cartan type, but my impression was that then
> it is called Lusztig involution. My plan is indeed to eventually implement
> the Lusztig involution in CrystalOfTableauxElements. What do you think?
That sounds like the right approach. Actually the Lusztig involution
wou
On Sun, Mar 27, 2011 at 11:07:58PM -0700, Anne Schilling wrote:
> On 3/27/11 6:27 PM, bump wrote:
> >>I just added a new patch on trac which implements the Schuetzenberger
> >>involution on both words and tableaux and also the promotion operator
> >>on tableaux of arbitrary shape:
> >>
> >>http://t
Dear Dan,
On 3/27/11 6:27 PM, bump wrote:
I just added a new patch on trac which implements the Schuetzenberger
involution on both words and tableaux and also the promotion operator
on tableaux of arbitrary shape:
http://trac.sagemath.org/sage_trac/ticket/10446
I have the impression this is f
> I just added a new patch on trac which implements the Schuetzenberger
> involution on both words and tableaux and also the promotion operator
> on tableaux of arbitrary shape:
>
> http://trac.sagemath.org/sage_trac/ticket/10446
I have the impression this is for Type A only. But the Schutzenberge
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