无多重性或仅含少量组分的约化Kronecker积
Reduced Kronecker products which are multiplicity free or contain only few components
摘要：
众所周知，如果增加所有三个分区的第一部分，则三个分区的克罗内克系数是有界且弱增加的序列。此外，如果分区λ、μ的第一部分足够大，则克罗内克积[λ][μ]= \sum_\ n g（λ，\m，\n）[v]的系数不依赖于第一部分，而仅依赖于其它部分。约化的Kronecker积[λ]_ \bullet \star [μ]_ \bullet可以（粗略地）看作Kronecker积[（n-1）]。|λ|，λ）][（n-|μ|，\m）]。本文对无重数的约化Kronecker积和分支数小于10的约化Kronecker积进行了分类，并给出了约化Kronecker积的分支数和分支数的一般下界.我们也给了一个下界的数量对组件的相应的分区不同的一个盒子。最后我们论证了两个约化Kronecker积相等仅在积的因子相同的平凡情形下才是可能的。
英文摘要：
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 λ,μare big enough then the coefficients of the Kronecker product [λ][μ]=\sum_\n g(ł,\m,\n)[ν] do not depend on the first part but only on the other parts. The reduced Kronecker product [λ]_\bullet \star[μ]_\bullet can be viewed (roughly) as the Kronecker product [(n-|λ|,λ)][(n-|μ|,\m)] for n big enough. In this paper we classify the reduced Kronecker products which are multiplicity free and those which contain less than 10 components.We furthermore give general lower bounds for the number of constituents and components of a given reduced Kronecker product. We also give a lower bound for the number of pairs of components whose corresponding partitions differ by one box. Finally we argue that equality of two reduced Kronecker products is only possible in the trivial case that the factors of the product are the same.
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