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.
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Fomin, S., Grigoriev, D., Nogneng, D. et al. On semiring complexity of Schur polynomials. comput. complex. 27, 595–616 (2018). https://doi.org/10.1007/s00037-018-0169-3
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DOI: https://doi.org/10.1007/s00037-018-0169-3