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Let $f(x) \in \mathbb{Z}[x]$ and suppose $f(\omega^j) \in \mathbb{Z}$ for all $j= 1, \dots, n$ where $\omega = e^{2 \pi i/n}$ is a primitive $n^{\text{th}}$ root of unity. Computational evidence ...

For $n \geq 1$, define the following operator $M_n$ on the ring of all polynomials with real coefficients. $$M_n P(x) = nP(x)^2 - x \int_0^x (P'(t))^2 \, \mathrm{d}t$$ Monomials $x^k$ are mapped to $n ...

Looking for references (insights) on a theory encompassing a notion of refined face polynomials and their associated refined h-polynomials that are generalizations of the relation between ordinary f-...

Fix a field $K$. Call a non-commutative polynomial $f(x_i)$ whose monomial terms are all of degree at least 2 in the variables $x_i$ magic if the finite dimensional $K$-algebra $A_{f,n}:=K<x_i>/(...

Revamped and updated on Sep 12, 2022: Given the complex coefficients $a_n$ of some generic formal power, Taylor, Laurent or other series, say the ordinary generating functions (o.g.f.) $f(z) = z +a_1 ...

The presentation given in Wikipedia for the infinite dihedral group is $$\langle r,s\mid s^2 =1, srs = r^{-1}\rangle.$$ Let $[R]$ denote the infinite set of reciprocal partition polynomials $R_n(u_1,...