On semiring complexity of Schur polynomials

Fomin, Sergey; Grigoriev, Dima; Nogneng, Dorian; Schost, Eric

doi:10.1007/s00037-018-0169-3

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On semiring complexity of Schur polynomials

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Grigoriev, Dima
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00037-018-0169-3
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arXiv:1608.05043.pdf
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Fomin, S., Grigoriev, D., Nogneng, D., & Schost, E. (2018). On semiring complexity of Schur polynomials. Computational Complexity, 27(4), 595-616. doi:10.1007/s00037-018-0169-3.

Cite as: https://hdl.handle.net/21.11116/0000-0003-FD47-1

Abstract

Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial {s_\lambda(x_1,\dots,x_k)} labeled by a partition {\lambda=(\lambda_1\ge\lambda_2\ge\cdots)} is bounded by
{O(\log(\lambda_1))} provided the number of variables $k$ is fixed.