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Article · International Mathematics Research Notices · November 25, 2022

Fundamental Invariants of Tensors, Latin Hypercubes, and Rectangular Kronecker Coefficients

Alimzhan Amanov, Damir Yeliussizov

Alimzhan Amanov
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Abstract

Abstract We study polynomial SL-invariants of tensors, mainly focusing on fundamental invariants that are of smallest degrees. In particular, we prove that certain 3-dimensional analogue of the Alon–Tarsi conjecture on Latin cubes considered previously by Bürgisser and Ikenmeyer implies positivity of (generalized) Kronecker coefficients at rectangular partitions and as a result provides values for degree sequences of fundamental invariants.

Advanced Combinatorial MathematicsTensor decomposition and applicationsAdvanced Algebra and Geometryfundamental invariantstensorsLatin hypercubes

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