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Question: Domino Tabloid (Tableaux) of shape A and type B

Question:Domino Tabloid (Tableaux) of shape A and type B

resolvent 593 Maple
January 01 2008
0
If any of the following has been programmed into Maple, then from a sufficient number of small examples, I might be able to "back-engineer" and figure out the solution to the following problem in general. I need help to know if I understand Ian Grant Macdonald's book "Symmetric Functions and Hall Polynomials" (1995, Clarendon Press, 2nd edition), page 109, correctly. I need to know what a domino tabloid of shape A and type B is, where A and B are both partitions of the positive integer N. I need to do this only for the case where A=(N), the partition of length 1. Essentially, I need the formula for the N-th powersum of the roots of a polynomial of degree D in terms of the elementary symmetric functions (the coefficients of the polynomial). The known determinantal formula given on page 28 of Macdonald's book, nor a recursion, will do, for what I need to do. Furthermore, I need (for now) to do it only on the simpler case of a trinomial, z^D + (-1)*e(D-s)*z^s + (-1)^D*e(D)=0 where e(D-s) = the (D-s)-the elementary symmetric function of the roots Thank you.
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