Hi All!
Is this a bug or a feature?
sage: [mu for mu in Partitions(6, min_slope=-2)]
[[6], [4, 2], [3, 3], [3, 2, 1], [3, 1, 1, 1], [2, 2, 2], [2, 2, 1,
1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]]
given that
sage: Partition([6,0])
[6]
That is, since sage follows the usual convention in ignoring trailing
zeros at the end of a partition the partition [6] does not have
min_slope=-2 so it shouldn't be in the list above. Similarly, [3,3]
should not appear.
For me the set of e-restricted partitions is the set of partitions
{ (mu_1,mu_2,...) | mu_i-\mu_{i+1}<e } which should coincide with
Partitions(min_slope=1-e) but it doesn't because of the behaviour
above. These partitions, or their conjugates, index the irreducible
modules of the Iwahori-Hecke algebras of type A at an e-th root of
unity.
I'm happy to fix this if it is deemed to be a bug, although I won't be
able to push anything until sage 5.0 when I hope to be able to compile
sage again on my lion infected mac. If it is not a bug then I am happy
to work around it.
Incidentally, irrespective of the answer to the above, the following
probably should not trigger an assertion error:
sage: Partitions(min_slope=-2)
---------------------------------------------------------------------------
AssertionError Traceback (most recent call
last)
/Users/andrew/Sage/<ipython console> in <module>()
/Applications/sage/local/lib/python2.6/site-packages/sage/combinat/
partition.pyc in Partitions(n, **kwargs)
3052 """
3053 if n is None:
-> 3054 assert(len(kwargs) == 0)
3055 return Partitions_all()
3056 else:
AssertionError:
Cheers,
Andrew
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