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

2022

Full text Open access: Green Metadata (CSL-JSON)
DOI 10.1093/imrn/rnac311
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

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.