Peter Bürgisser ; Christian Ikenmeyer - The complexity of computing Kronecker coefficients

dmtcs:3622 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3622
The complexity of computing Kronecker coefficientsArticle

Authors: Peter Bürgisser 1; Christian Ikenmeyer 1

  • 1 Mathematisches Institut der Universität Paderborn

Kronecker coefficients are the multiplicities in the tensor product decomposition of two irreducible representations of the symmetric group $S_n$. They can also be interpreted as the coefficients of the expansion of the internal product of two Schur polynomials in the basis of Schur polynomials. We show that the problem $\mathrm{KRONCOEFF}$ of computing Kronecker coefficients is very difficult. More specifically, we prove that $\mathrm{KRONCOEFF}$ is #$\mathrm{P}$-hard and contained in the complexity class $\mathrm{GapP}$. Formally, this means that the existence of a polynomial time algorithm for $\mathrm{KRONCOEFF}$ is equivalent to the existence of a polynomial time algorithm for evaluating permanents.


Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)
Section: Proceedings
Published on: January 1, 2008
Imported on: May 10, 2017
Keywords: representations of symmetric groups,tensor products,Kronecker coefficients,computational complexity,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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