5 problems

Let $\hat R^+$ be the set of positive affine roots, let $\hat\rho$ be the affine Weyl vector, let $k$ be the parameter in the definition of the affine Macdonald polynomials, and le…

Let $k$ be a nonnegative integer, let $x=(x_1,\dots,x_n)$, and let $\ddot{e}_r(x)$ denote the notation used in the source. Additional type B affine Jacobi–Trudi conjecture. With…

Let $k$ be a nonnegative integer, let $x=(x_1,\dots,x_n)$, and write $\dot{e}_r(x)=e_r(x^{\pm})$. For the type $\mathrm{B}_n$ Hall–Littlewood polynomial…

Affine compatibility-degree conjecture. We have

Adjacent biconvex subsets conjecture. A pair $(A,B)$ of biconvex subsets is adjacent if and only if there is a root $\beta$, real or imaginary, such that $(A,B)$ is $\beta$-adjacen…