# Tagged Questions

**1**

vote

**1**answer

101 views

### Truncated sums of symmetric polynomials; reference request for an algebraic derivation

EDIT: This is a case of being too wrapped up in a formulation
($e_j,p_i,$ and the like) to try something simple. It did not
occur to me to pull exp to the outside in the weeks I have
stared at this. ...

**3**

votes

**2**answers

318 views

### Counting polynomials with same coefficient sum and a given value at a point

Call an univariate polynomial $f(x) = \sum_{i=0}^{n}a_{i}x^{i} \in \Bbb{Z}[x]$ symmetric if $a_{i} = a_{n-i}$ and $a_{0} = a_{n} > 0$.
For a given $\sum_{i=0}^{n}a_{i}$ and $a_{i} \geq 0$, how ...

**0**

votes

**0**answers

85 views

### Enumerating certain bounded polynomials with partition type property constraints

Let $p(x) = a_{0} + a_{1}x + a_{2}x^{2} + \dots + a_{d}x^{d} + \dots + a_{2d+\alpha}x^{2d+\alpha} \in \mathbb{Z}[x]$ where $\alpha \in \{0,1\}$ with the constraints
$(1)$ $0 \leq ...