33 problems

Let $\lambda$ be a partition with $n$ outside corners. Choose a corner $k$ and corresponding weight $\omega_\ell$, and retain the notions of Theorem … 1leq i1<cdots<irleq kleq jr<c…

Let ${\bf T}_n$ be the set of standard Young tableaux with $n$ boxes, let $I_T$ be the primitive ideal attached to $T$, let ${\mathcal V}_T$ be its orbital variety, and let…

Let $k, ell\ge 0$ and $\beta,z>0$. Define … and let $r_{(k,\ell),\beta}(z)$ be the corresponding limiting integral ratio. Second-term oscillation conjecture. As $n\to\infty$, the q…

Let $\lambda=(\lambda_1,\ldots,\lambda_r)\in\Lambda_m$ be a Young diagram with $\lambda_1$ boxes in its first row, and let $\lambda^{(n)}$ be obtained by adding a first row of $n$…

Let $\Delta^{k,m}$ be the star graph with $k$ branches, each receiving $m$ labeled chips, and consider the random labeled chip-firing process in which every firable vertex is equal…

Under the Robinson–Schensted–Knuth correspondence, a permutation is mapped to a pair of Young tableaux of the same shape. Let $A$ be the set of permutations whose tableaux avoid th…

Let $k\geq 1$ and let $T\in\operatorname{YT}(n)$, where $n\geq k+4$. Here $\operatorname{mM}_k(T)$ denotes the multiset of $k$-minors of the standard Young tableau $T$. Multiset re…

Let $k\geq 2$ and let $T\in\operatorname{YT}(n)$, where $n\geq k^2+2k$. Here $\operatorname{M}_k(T)$ denotes the collection of $k$-minors of the standard Young tableau $T$. Reconst…

Let $\Omega$ be the open diamond … and let $\Phi$ be the limiting variational function for a homogeneous Poisson point process on $\Omega$; its derivative $\Phi'$ is the correspond…

Scrollar-invariant tableau conjecture. The multiset of scrollar invariants of the partition $\lambda$ with respect to $\varphi$ is

Pathwise asymptotic enumeration conjecture. As $n_N\to\infty$ and $\varepsilon\to0$,

The variational principle for skew Young tableaux. The function $g(t,x)$ maximizes

Balanced-partition product conjecture. If $\lambda$ is balanced, then

Converse CDE conjecture. The interval $[\emptyset,\lambda]$ has the CDE property if and only if $\lambda$ is balanced.

TVK-shape sorting-probability conjecture. There is a universal constant $C>0$ such that

Higher Specht basis conjecture. The set of polynomials

For $n\geq 2$, let $\operatorname{SYT}(\delta_n)$ be the set of standard Young tableaux of staircase shape $\delta_n$, let $\operatorname{SN}_n$ be the set of sorting networks on…

For $n\ge 2$, let $\delta_n$ be the staircase Young diagram, let $\operatorname{SYT}(\delta_n)$ be its standard Young tableaux, and let $\operatorname{SN}_n$ be the set of sorting…

Let $n$ be a positive integer, let $abla$ be the nabla operator on symmetric functions, and let $en$ and $s{mu}$ denote the elementary and Schur symmetric functions, respectively.…

Let $S,T\in\mathcal{T}(n,n)$ be standard Young tableaux of shape $(n,n)$, and let $a_i$ and $b_i$ denote the entries in the first row of $S$ and $T$, respectively. Characterization…

Let $\mathcal{T}(n,n)$ be the set of standard Young tableaux of shape $(n,n)$, let $\{v_T:T\in\mathcal{T}(n,n)\}$ and $\{w_S:S\in\mathcal{T}(n,n)\}$ be the tableau and web bases of…

Let $w$ be a permutation and let $a_{w,\lambda}$ denote the corresponding Edelman–Greene coefficient for a partition $\lambda$, with $f^{\lambda}$ the number of standard Young tabl…

Let $F(h,k)$ be the large-$N$ limit … where $F_N(h,k)$ is the joint moment considered in the paper. For a Young diagram $\lambda$, write $|\lambda|$ for its size, $\lambda_1$ for i…

A barely set-valued semistandard Young tableau is a set-valued semistandard Young tableau in which exactly one square is assigned two integers and every other square is assigned a…

Edelman–Greene height conjecture. The word $\mathrm{EG}^{-1}(Q)$ is a maximal element of $\mathcal{P}_Q$, and