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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