59 problems

Let $\lambda,\mu,\nu$ be partitions with $|\lambda|+|\mu|=|\nu|$, and let $c^{\nu}_{\lambda\mu}$ be the Littlewood–Richardson coefficient, the multiplicity of the Schur function…

Let $P(N)$ be the stretched Littlewood–Richardson polynomial associated with fixed partitions, so that $P(N)=c^{N\nu}_{N\lambda,N\mu}$ for positive integers $N$. Fulton's conjectur…

Okounkov's conjecture. The function

Let $c_{\mu\nu}^{\lambda}$ be the Littlewood–Richardson coefficient in the product expansion for a family $\mathcal F$ of interpolation polynomials, and let…

Let $\lambda$, $\mu$, and $\nu$ be partitions whose Young diagrams fit in a $p$ by $n-p$ rectangle, and suppose the corresponding Littlewood–Richardson number is positive. For thre…

Let $c^\lambda_{\mu\nu}$ be a Littlewood–Richardson coefficient, and let $\textsc{ComputeLR}$ be the problem of computing it from partitions $\lambda,\mu,\nu$. Pak–Panova conjectur…

Let $n$ be a positive integer, let $clambda$, $cmu$, and $cnu$ be partitions of length at most $n$, and let $T_n$ consist of the triples for which $V_\nu$ occurs in…

In the exceptional Hermitian symmetric case $G_{\Bbb R}=E\,VII$, one has $(\frak g,\frak k)=(\frak e_7,\frak e_6\oplus{\Bbb C})$ and rank $r=3$. Let $\Lambda$ be the set of partiti…

Let $G_{\Bbb R}/K_{\Bbb R}$ be an irreducible Hermitian symmetric space of rank $r$, let $X=\frak p^+$, and let $\Lambda$ be the set of partitions of length at most $r$. For…

Let $G=GL_n$, let $I$ specify a Levi subgroup, and let $K_{\lambda,\mu}^{GL_n,I}(q)$ be the corresponding Kostant-type $q$-analogue of the generalized Littlewood–Richardson coeffic…

Given an ordered pair $(\lambda,\mu)$ of partitions with the same number of parts, define … and … For any partition $\nu$, the starred-transformation conjecture. … This is a combin…

Saturation conjecture. If there exists a positive integer $k$ such that

Let $(\mu_1,\nu_1,\lambda_1)$ and $(\mu_2,\nu_2,\lambda_2)$ be triples of partitions differing by a single box move, with pivot boxes $b_1\in\sigma_1$ and $b_2\in\sigma_2$ whose…

Let shifted Jack Littlewood–Richardson coefficients be defined for partitions with $|\lambda|\leq|\mu|+|\nu|$. Shifted Jack congruence conjecture. The adjacent-triple congruence co…

Let $(\mu_1,\nu_1,\lambda_1)$ and $(\mu_2,\nu_2,\lambda_2)$ be adjacent triples of partitions corresponding to a pivot at $b$. Let $\mathcal W'$ and $\mathcal W$ be the associated…

Let $T$ be a triple of partitions and let $W$ be a window for $T$. A rule is a Stanley sum whose evaluation gives the corresponding Jack Littlewood–Richardson coefficient. Jack win…

Let $\bm g_{\star}=\bm g_{21,21}^{321}$ be the specified Stanley sum, and let $\mathcal W$ be the seven-parameter window family with window factor $F_W$. Seven-parameter window-fam…

For partitions $\mu,\nu,\lambda$, let $\mathsf{SD}_{\mu\nu}^{\lambda}$ be the set of Stanley diagrams and let a Stanley sum be an integer linear combination of these diagrams. Stan…

Let $c_{\mu\nu}^{\lambda}$ be the ordinary Littlewood–Richardson coefficient. For a triple of partitions $(\mu,\nu,\lambda)$, let $\mathsf{SD}_{\mu\nu}^{\lambda}$ denote the set of…

Let $(\mu_1,\nu_1,\lambda_1)$ and $(\mu_2,\nu_2,\lambda_2)$ be triples of partitions that differ by a single box move in one pair, with pivot boxes $b_1\in\sigma_1$ and…

Let two triples of partitions be adjacent when they differ by a single box move in one of the pairs, and let the move identify a shared hook length. Hook divisibility conjecture. T…

Let $g_{\mu\nu}^{\lambda}(\alpha)$ be Jack Littlewood–Richardson coefficients, and let the associated polynomials be those introduced for triples of partitions and their adjacent t…

Fix partitions $\mu$ and $\nu$. For each family $\mathcal F$, let … and let $M_{\mu\nu}$ be the set of partitions $\lambda\supseteq\mu,\nu$ for which there exists a Molev tableau o…

Regular factorization conjecture. For certain factorizations $\kappa$, there exist factorization solutions for which

Factorization conjecture. The Jack Littlewood–Richardson coefficient has an expansion