80 problems

Let $R$ be a sequence of rectangles. Let $b_R:RC(\lambda^t;R^t)\to CST(\lambda,\gamma(R))$ be the restriction of the inverse rigged-configuration bijection to the indicated subset,…

Staircase flagged-tableaux cyclic sieving conjecture. The triple $(\mathrm{FT}(sc_n,b),\langle\operatorname*{Pro}\rangle,Cat_{\ell}(x))$ exhibits the cyclic sieving phenomenon.

Type C K-Stanley expansion conjecture.

Let $\omega$ be the permutation governing the switching algorithm, and let $\mathcal{O}\in\operatorname{Orb}(\omega)$ be one of its orbits. A genomic tableau is a tableau counted b…

K-jdt–Buch insertion conjecture. The K-jdt rectification of $T \ast S$ is the same tableau as the Buch insertion of $T$ into $S$.

The stronger factor-sequence conjecture. Under these hypotheses, $(\dots,X',Y',\dots)$ is also a factor sequence for $\gamma$.

Let $R\trianglerighteq R'$ be a covering relation in the dominance order on sequences of rectangles. Let $\theta_R^{R'}:LRT(\lambda;R)\to LRT(\lambda;R')$ be the embedding obtained…

Let $R$ be a sequence of rectangles, and let $CT(\lambda;R)$ and $CCT(\lambda^t;R^t)$ denote the row- and column-catabolizable tableaux defined in the source. Catabolizable transpo…

Let $R$ be a sequence of rectangles such that $R^t$ is dominant. Let $b_R$ be the map from rigged configurations to tableaux, and let $CCT(\lambda;R)$ denote the set of $R$-column-…

Let $R$ be a sequence of rectangles, let $\widetilde{R}$ and $\widetilde{\lambda}$ be the complementary dual data defined in the source, and let $\operatorname{dual}$ be the corres…

Let $\operatorname{ev}$ be evacuation on column-strict tableaux, restricting to a bijection $LRT(\lambda;R)\to LRT(\lambda;\operatorname{rev}(R))$. Let $\theta$ complement each rig…

Let $R$ be a sequence of rectangles and let $u$ be a permutation of the rectangle indices. The bijection $u_R:LRT(\lambda;R)\to LRT(\lambda;uR)$ is defined by composing the adjacen…

Let $R$ be a dominant sequence of rectangles. Let $LRT(\lambda;R)$ be the corresponding Littlewood–Richardson tableaux, let $RC(\lambda^t;R^t)$ be the rigged configurations, and le…

Let $\mathfrak{g}$ be of type $C_n$, let $\lambda/\mu$ be a skew diagram, and let $\chi_{\lambda/\mu,a}$ be the associated Jacobi–Trudi determinant for $a\in\mathbb{C}$. Let…

Fix positive integers $m,n$ and set $\delta_n=(n-1,n-2,\ldots,1,0)$. Let $E_{n,k}$ be defined by … and let $D_n^{(m),\lambda}(z;q)$ denote the generalized tableau sum associated wi…

Fix positive integers $m,n$ and set $\delta_n=(n-1,n-2,\ldots,1,0)$. For a partition $\lambda\subseteq m\delta_n$, let $T$ be a semistandard tableau of shape…

The refined shuffle conjecture. For $1\leq k\leq n$,

Fix $n$ and let $\delta_n=(n-1,n-2,\ldots,1,0)$. For a partition $\lambda\subseteq\delta_n$, let $T$ range over semistandard tableaux of skew shape $(\lambda+(1^n))/\lambda$, and l…

Let $\lambda$ be a partition with $\ell$ parts and fixed parity for each part. Let $G_\lambda(x/x)$ be the specialized symmetric function defined by substituting $2p_{2i-1}$ for…

A Demazure crystal is denoted by $\mathcal{B}_{w,\lambda}$, where the crystal is of type $A$, normal, and finite. A flagged skew tableau crystal is the crystal of flagged skew tabl…

Let $a,b\geq2$ be positive integers, let $\gamma=(a,2,2,\ldots,2,b)$, and let $K_\gamma$ be the corresponding K-chain with associated poset $P$. K-chain powerful-tableau formula co…

Let $\mathbf{m}\in\mathbb{E}_n$, let $\lambda\vdash n$, and let $T\in\operatorname{HikSYT}(\mathbf{m},\lambda)$. For the recursively defined Hikita weight $h_T(q)$ and every real…

Let $\mathbf{m}\in\mathbb{E}_n$, let $P=P_{\mathbf{m}}$ be the associated natural unit interval order, and let $\lambda\vdash n$. Let $\operatorname{strongST}_P(\lambda)$ be the st…

Let $P$ be a $(\mathbf{3}+\mathbf{1})$-free poset, let $\lambda\vdash n$, and let $m_\lambda^P(\mathbf{u})$ be the relevant noncommutative elementary coefficient in…

Let $P$ be a $(\mathbf{3}+\mathbf{1})$-free poset, let $\lambda$ be a partition, and let $c_\lambda^P$ be the corresponding elementary-basis coefficient of…