I was trying to list the King tableaux of a particular shape. Here's the
function:
def list_of_king_tableaux(t_shape, t_max_entry):
"""A function which finds the list of King tableaux of given shape."""
return list([t for t in SemistandardTableaux(t_shape,
max_entry=t_max_entry) if is_king_tableau(t)])
And this is the output I got:
sage: list_of_king_tableaux([2,2],4)
[[[1, 1], [3, 3]],
[[1, 1], [3, 4]],
[[1, 1], [4, 4]],
[[1, 2], [3, 3]],
[[1, 2], [3, 4]],
[[1, 2], [4, 4]],
[[1, 3], [3, 4]],
[[1, 3], [4, 4]]]
The list shows the tableaux that are not king tableaux. How do I choose the
ones that obey the king tableaux condition?
On Monday, March 9, 2020 at 4:54:48 AM UTC-4, Bruce wrote:
>
> The king_tableaux is an iterator not a function.
> it is used in the last three lines.
>
> if you want a list look inside no_of_king_tableaux
>
> On Sunday, 8 March 2020 21:41:34 UTC, Soheli Das wrote:
>>
>> Thank you Bruce!! Indeed the function looks tidier.
>> The third function gives me this message: "<generator object
>> king_tableaux at 0x6ffea35729a8>". The 'p' is supposed to mean the
>> partition right?
>>
>> Once again thank you for your help. I really appreciate it!
>>
>> -Soheli
>>
>> On Sunday, March 8, 2020 at 5:26:41 AM UTC-4, Bruce wrote:
>>>
>>> Thank you for helping me. I created the function:
>>>
>>> sage: def is_king_tableau(t,no_of_rows):
>>> ....: for i in range(no_of_rows):
>>> ....: if t[0][0] != 1:
>>> ....: return False
>>> ....: elif t[i][0] <= 2*i:
>>> ....: return False
>>> ....: else:
>>> ....: i=i+1
>>> ....: return True
>>>
>>>
>>> I have tidied up your function and written some simple functions to show
>>> how it is used.
>>> I hope this will encourage you to learn more about Python, make further
>>> improvements and write your own functions.
>>>
>>> The last three lines are not a function but use the iterator to show the
>>> motivation for the definition of a King tableau.
>>>
>>> def is_king_tableau(t):
>>> """A function which tests if a semistandard tableau is a King
>>> tableau."""
>>> if t[0][0] != 1:
>>> return False
>>> for i, row in enumerate(t):
>>> if row[0] <= 2*i:
>>> return False
>>> return True
>>>
>>> def no_of_king_tableaux(p):
>>> """A function which finds the number of King tableaux of given
>>> shape."""
>>> return len([t for t in SemistandardTableaux(p) if
>>> is_king_tableau(t)])
>>>
>>> def king_tableaux(p):
>>> """An iterator for the set of King tableaux of given shape."""
>>> for t in SemistandardTableaux(p):
>>> if is_king_tableau(t):
>>> yield t
>>>
>>> for t in king_tableaux([2,2]):
>>> t.to_Gelfand_Tsetlin_pattern().pp()
>>> print "\n"
>>>
>>
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