A Kronecker coefficient counts the number of times a representation of a symmetric group occurs in the tensor product of two others. Finding a fast algorithm to determine when a Kronecker coefficient is positive is an open problem. There has been an increased interest in this problem over the last few years as it comes up in the geometric approach to the complexity conjecture P = NP due to Mulmuley and Sohoni. I will explain how a higher dimensional analogue of the Robinson–Schensted–Knuth correspondence relates Kronecker coefficients to the problem of counting the number of integer arrays with specified slice sums.

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Last updated: 01 Oct 2023