论文标题
估计和计算Kronecker系数：矢量分区函数方法
Estimating and computing Kronecker Coefficients: a vector partition function approach
论文作者
论文摘要
我们通过Mishna，Rosas和Sundaram描述的公式来研究Kronecker系数$ g_ {λ，μ，ν} $，其中系数表示为矢量分区函数函数评估的签名总和。特别是，我们使用此公式来确定以$λ，μ$和$ν$的长度来评估，绑定和估计$ g_ {λ，μ，ν} $。我们用$ \ ell（μ）\ leq 2，\ \ ell（ν）\ leq 4，\ el \ ell（λ）\ leq 8 $描述了计算Kronecker系数$ g_ {λ，μ，ν} $的计算工具。我们通过与单个矢量分区函数评估给出的相关原子kronecker系数的消失，为Kronecker系数提供了一组新的消失条件。我们为任何积极的整数$ m，n $提供了Kronecker Polyhedron的稳定面孔。最后，我们在原子kronecker系数和kronecker系数上给出了上限。
We study the Kronecker coefficients $g_{λ, μ, ν}$ 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 use this formula to determine formulas to evaluate, bound, and estimate $g_{λ, μ, ν}$ in terms of the lengths of the partitions $λ, μ$, and $ν$. We describe a computational tool to compute Kronecker coefficients $g_{λ, μ, ν}$ with $\ell(μ) \leq 2,\ \ell(ν) \leq 4,\ \ell(λ) \leq 8$. We present a set of new vanishing conditions for the Kronecker coefficients by relating to the vanishing of the related atomic Kronecker coefficients, themselves given by a single vector partition function evaluation. We give a stable face of the Kronecker polyhedron for any positive integers $m,n$. Finally, we give upper bounds on both the atomic Kronecker coefficients and Kronecker coefficients.
