What is a Schur function indexed by a sequence which
is not a partition?

Exercise: In the Jacobi-Trudi defintion, it is not necessary that the indexing 

sequence be a partition.  Our function ehp2s will expand this in the Schur

basis (which is indexed by a partition).  What happens?

> peh2s(Schur_in_h([3,2,1]));

> peh2s(Schur_in_h([2,3,1]));

> peh2s(Schur_in_h([2,4,1]));

> peh2s(Schur_in_h([3,4,1]));

> peh2s(Schur_in_h([2,5,3]));

> peh2s(Schur_in_h([1,1,5]));

> peh2s(Schur_in_h([2,1,5]));

> peh2s(Schur_in_h([3,1,5]));

> peh2s(Schur_in_h([2,2,5]));

> peh2s(Schur_in_h([5,1,4]));

Conjecture 1: The answer is always +/-/0 times a single Schur function

Conjecture 2: If the indexing sequence contains an [....,n,n+1,....] then the answer is 0

Conjecture 3: If there is only one exchange of number to make the sequence decreasing
then the answer is negative.

Exercise: Conjecture/prove/predict what Schur function appears and when the answer is 0.