3 problems

Let $\{\lambda^n/\mu^n\}$ be a graded skew partition sequence, and for each $n\geq0$ set $u_n=P_{\lambda^n/\mu^n}$. A skew diagram $\lambda^n/\mu^n$ is column-connected if it canno…

Hall–Littlewood immaculate positivity conjecture. The element $\mathcal{Q}'_\lambda$ expands in the immaculate basis with coefficients that are positive polynomials in $q$. More ex…

Generalized Lascoux positivity conjecture. Both functions are positive, up to a global sign, in the basis of the $k^\prime$-Schur functions, with coefficients expressed in the para…