# Finding absent partitions in polynomials using SageMath

The full details of the hybrid math/coding problem of interest to me are presented in the MathOverflow question "Outlier absences of monomials in a group of inversion partition polynomials". In order to develop code that would determine which monomials are absent in higher order polynomials, I need some pointers to Sage documentation/example code on

1) library calls to handle the relevant math

2) introducing an array for $K$ indeterminants $a_k$, or $a(k)$, of a polynomial $p(x) = 1 + \sum_{k = 1}^{K} a(k) * x^k/factorial(k)$

3) code for determining the absence of monomials/partitions of n in the partition polynomials RT_n derived through the transformations described in the MO-Q, of which the first few are illustrated in the MO-Q.

The crude SageMath code (my first) given in the MO-Q generates the first few partition polynomials, but identification of absent monomials was done by inspection of the results and comparison with other partition polynomials which contain the full panoply of partitions, e.g., the sets [E] and [P] given in the MO-Q.

Can someone direct me to relevant Sage documentation that would allow me to develop the code?