9 problems

k-Schur Pieri conjecture. One has

Let $s_\Lambda$ be a Schur superpolynomial indexed by a superpartition, and let $(;r)$, $(r;)$, $(;1^r)$ and $(0;1^r)$ denote the corresponding bosonic and fermionic row and column…

Dual immaculate Pieri conjecture. The dual quasisymmetric basis should satisfy a signed multiplicity-free Pieri rule.

Signed left Pieri conjecture. There is a statistic $\operatorname{sign}(\alpha,\beta)$ such that

Dual immaculate Pieri conjecture. The dual immaculate basis has a multiplicity-free signed Pieri rule; explicitly,

The signed left Pieri rule. The product has the form

Let $\lambda$ and $\mu$ be partitions with $\mu \subseteq \lambda$, and let $r\geq0$. For a horizontal strip $\alpha/\beta$, define … For a broken ribbon $\alpha/\beta$, define…

Let $\lambda$ and $\mu$ be partitions with $\mu \subseteq \lambda$, and let $r\geq 0$. Write $e_r=P_{1^r}$. For a vertical strip $\alpha/\beta$, define … where…

Let $\lambda$ and $\mu$ be partitions with $\mu \subseteq \lambda$, and let $r\geq 0$. For a skew shape $\alpha/\beta$, write $\operatorname{sk}(\alpha/\beta)$ for the coefficient…