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Topic: Differential Resolvents
Replies: 0

 John Nahay Posts: 104 Registered: 12/6/04
Differential Resolvents
Posted: Jul 1, 1996 2:57 AM

I am working on a dissertation in math at Rutgers University. My goal is
to find as simple a formulae as possible for the linear, differential
equation of order N with x as dependent variable, y as independent
variable, and y=P(x) is a polynomial in x of degree N, P(0)=0. This
linear ODE is called the "differential resolvent" (DR) of the polynomial,
P. The coefficient functions making up DR are polynomials in y and the
coefficients of P. The gcd of these polynomials is 1.

In the course of this work, I need many steps. Here are two of them:
I hope these are not elementary combinatorical problems.

1) Given positive integers n and k, how many partitions of n with no part
bigger than k exist?

2) Given partitions, P and Q, how many domino (brick) tabloids are there
of shape P and type Q, as a function of the parts of P and Q?

John Nahay