Questions tagged [laurent-polynomials]

This question is motivated by Richard Stanley's A question on the Laurent phenomenon (motivated by his answer to the question what is the probability that a scissor became the champion?). He asked ...

Let $L$ be a Laurent polynomial with real coefficients, i.e., $$L(z)=\sum_{j=-r}^{s}a_{j}z^{j},$$ where $r,s\in\mathbb{N}$ and $a_{j}\in\mathbb{R}$. Assume further that the set $L^{-1}(\mathbb{R})\...

To deal with root systems of type B C D, one needs to understand symmetric Laurent polynomials $\Lambda$. I am wondering if the naive definition of power sum symmetric Laurent polynomials form a basis ...

To a given a Laurent polynomial $f$ over the field of Puiseux seris with parameter $t$, $f \in \mathbb{C} \lbrace\lbrace t \rbrace\rbrace[z_1^{\pm1},...,z_n^{\pm 1}]$, one can associate the ...

Let $R$ be a Noetherian domain, and let $D$ denote its division ring. Define $S = D_q[x_1^{\pm 1}, x_2^{\pm 1}]$ as an iterated skew-Laurent polynomial ring with the relation $x_1 x_2 = q x_2 x_1$. Is ...

Let $A := \mathbb{K}_{\Lambda}[x_1^{\pm 1}, x_2^{\pm 1}, x_3^{\pm 1}, x_4^{\pm 1}]$, $B := \mathbb{K}_{\Lambda'}[x_1^{\pm 1}, x_2^{\pm 1}, x_3^{\pm 1}]$, and $C := \mathbb{K}_{\Lambda''}[x_1^{\pm 1}, ...