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On the complexity of computing Kronecker coefficients

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Abstract

We study the complexity of computing Kronecker coefficients \({g(\lambda,\mu,\nu)}\). We give explicit bounds in terms of the number of parts \({\ell}\) in the partitions, their largest part size N and the smallest second part M of the three partitions. When M =  O(1), i.e., one of the partitions is hook-like, the bounds are linear in log N, but depend exponentially on \({\ell}\). Moreover, similar bounds hold even when \({M=e^{O(\ell)}}\). By a separate argument, we show that the positivity of Kronecker coefficients can be decided in O(log N) time for a bounded number \({\ell}\) of parts and without restriction on M. Related problems of computing Kronecker coefficients when one partition is a hook and computing characters of S n are also considered.

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  1. Mathematics Department, UCLA, Los Angeles, CA, 90095, USA

    Igor Pak

  2. Mathematics Department, University of Pennsylvania, Philadelphia, PA, 19104, USA

    Greta Panova

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Pak, I., Panova, G. On the complexity of computing Kronecker coefficients. comput. complex. 26, 1–36 (2017). https://doi.org/10.1007/s00037-015-0109-4

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