Related papers: Upper bounds on Kronecker coefficients with few ro…

We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove $k$-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound…

We study the Kronecker coefficients $g_{\lambda, \mu, \nu}$ via a formula that was described by Mishna, Rosas, and Sundaram, in which the coefficients are expressed as a signed sum of vector partition function evaluations. In particular, we…

We resolve three interrelated problems on \emph{reduced Kronecker coefficients} $\overline{g}(\alpha,\beta,\gamma)$. First, we disprove the \emph{saturation property} which states that $\overline{g}(N\alpha,N\beta,N\gamma)>0$ implies…

We resolve two open problems on Kronecker coefficients $g(\lambda,\mu,\nu)$ of the symmetric group. First, we prove that for partitions $\lambda,\mu,\nu$ with fixed Durfee square size, the Kronecker coefficients grow at most polynomially.…

We give formulae for computing Kronecker coefficients occurring in the expansion of $s_{\mu}*s_{\nu}$, where both $\mu$ and $\nu$ are nearly rectangular, and have smallest parts equal to either 1 or 2. In particular, we study…

We present a lower bound on the Kronecker coefficients for tensor squares of the symmetric group via the characters of~$S_n$, which we apply to obtain various explicit estimates. Notably, we extend Sylvester's unimodality of $q$-binomial…

Weprovide an upper bound for generalized Littlewood-Richardson coefficients $c^w_{uv}$, where $u$ is a two-row Young diagram corresponding to a Grassmannian permutation. We end with a conjecture on the upper bounds for all such structure…

Given a skew diagram $\gamma/\lambda$, we determine a set of lower and upper bounds that a partition $\mu$ must satisfy for Littlewood-Richards coefficients $c^{\gamma}_{\lambda,\mu}>0$. Our algorithm depends on the characterization of…

We study the complexity of computing Kronecker coefficients $g(\lambda,\mu,\nu)$. We give explicit bounds in terms of the number of parts $\ell$ in the partitions, their largest part size $N$ and the smallest second part $M$ of the three…

We show that the problem of deciding positivity of Kronecker coefficients is NP-hard. Previously, this problem was conjectured to be in P, just as for the Littlewood-Richardson coefficients. Our result establishes in a formal way that…

We give explicit positive combinatorial interpretations for the plethysm coefficients $\langle s_\mu[s_\nu], s_\lambda\rangle$, when $\lambda$ has at most two rows, as counting certain marked trees. In the special case $\mu=(n)$, this also…

The Kronecker coefficients are the structural constants for the tensor categories of representations of the symmetric groups; namely, given three partitions $\lambda, \mu, \tau$ of $n$, the multiplicity of $\lambda$ in $\mu \otimes \tau$ is…

We give new bounds and asymptotic estimates for Kronecker and Littlewood--Richardson coefficients. Notably, we resolve Stanley's questions on the shape of partitions attaining the largest Kronecker and Littlewood--Richardson coefficients.…

It is known that the Kronecker coefficient of three partitions is a bounded and weakly increasing sequence if one increases the first part of all three partitions. Furthermore if the first parts of partitions \lambda,\mu are big enough then…

Various upper and lower bounds are provided for the (angular) Kronecker constants of sets of integers. Some examples are provided where the bounds are attained. It is proved that 5=16 bounds the angular Kronecker constants of 3-element sets…

The Kronecker coefficients and the Littlewood-Richardson coefficients are nonnegative integers depending on three partitions. By definition, these coefficients are the multiplicities of the tensor product decomposition of two irreducible…

We prove an inequality for the Kostka-Foulkes polynomials $K_{\lambda ,\mu}(q)$. As a corollary, we obtain a nontrivial lower bound for the Kostka numbers and a new proof of the Berenstein-Zelevinsky weight-multiplicity-one-criterium.

We give upper and lower bounds on the leading coefficients of the $L^2$-Alexander torsions of a $3$-manifold $M$ in terms of hyperbolic volumes and of relative $L^2$-torsions of sutured manifolds obtained by cutting $M$ along certain…

We find and prove a factorization formula for certain Macdonald Littlewood-Richardson coefficients $c_{\lambda\mu}^{\nu}(q,t)$. Namely, we consider the case that the Kostka number $K_{\mu, \nu -\lambda}$ is $1$. This settles a particular…

We settle the question of where exactly the reduced Kronecker coefficients lie on the spectrum between the Littlewood-Richardson and Kronecker coefficients by showing that every Kronecker coefficient of the symmetric group is equal to a…