A Cartesian decomposition of a coherent configuration✗is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set.It turns out that every tensor decomposition of✗comes from ...A Cartesian decomposition of a coherent configuration✗is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set.It turns out that every tensor decomposition of✗comes from a certain Cartesian decomposition.It is proved that if the coherent configuration✗is thick,then there is a unique maximal Cartesian decomposition of✗;i.e.,there is exactly one internal tensor decomposition of✗into indecomposable components.In particular,this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations.A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.展开更多
基金The first author was supported by the National Natural Science Foundation of China(Grant No.11971189).
文摘A Cartesian decomposition of a coherent configuration✗is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set.It turns out that every tensor decomposition of✗comes from a certain Cartesian decomposition.It is proved that if the coherent configuration✗is thick,then there is a unique maximal Cartesian decomposition of✗;i.e.,there is exactly one internal tensor decomposition of✗into indecomposable components.In particular,this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations.A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.
