3 problems

Positivity conjecture. The coefficients in these Schur-basis expansions are polynomials with nonnegative integer coefficients.

Let $R=(R_1,\ldots,R_p)$ be a dominant sequence of rectangular partitions, and let $\Lambda$ be the partition with empty $p$-core and $p$-quotient $(R_1,\ldots,R_p)$. The polynomia…

Let $\lambda$ be a partition of size $k$, and let $s_\lambda({\mathbf u})$ and $h_\lambda({\mathbf u})$ be the non-commutative Schur and homogeneous symmetric functions in the ribb…