Tensor products of coherent configurations |
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Authors: | Gang CHEN Ilia PONOMARENKO |
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Affiliation: | 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China2. Steklov Institute of Mathematics at St. Petersburg, Russia3. Sobolev Institute of Mathematics, Novosibirsk, Russia |
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Abstract: | 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. |
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Keywords: | Coherent configuration Cartesian decomposition Krull–Schmidt theorem |
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