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straighten -- computes straightening of a tableau



If a hashtable h is provided, then this outputs nothing, it simply just modifies h. When looking up values, remember that the keys are stored with rows weakly increasing. If no hashtable is provided, then the user is simply given the straightening of the tableau in terms of semistandard tableaux. The answer is in the form a hashtable: each key is a semistandard tableaux, and the value of the key is the coefficient of that semistandard tableaux used to write the input t as a linear combination.
i1 : h = new MutableHashTable from {}

o1 = MutableHashTable{}

o1 : MutableHashTable
i2 : straighten({{3,4}, {1,2}}, h)
i3 : h#{{3,4}, {1,2}} -- get the coefficients

o3 = HashTable{{{1, 2}, {3, 4}} => 1}

o3 : HashTable
i4 : straighten({{3,4}, {1,2}}) -- just get the answer instead

o4 = HashTable{{{1, 2}, {3, 4}} => 1}

o4 : HashTable

Ways to use straighten :

For the programmer

The object straighten is a method function.