On semiring complexity of Schur polynomials

Sergey Fomin; Dima Grigoriev; Dorian Nogneng; Eric Schost

On semiring complexity of Schur polynomials

Computational Complexity 2018-05-22 v2 Combinatorics

Authors: Sergey Fomin , Dima Grigoriev , Dorian Nogneng , Eric Schost

Abstract

Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that when the number of variables is fixed, the semiring complexity of a Schur polynomial $s_\lambda$ is $O(log(\lambda_1))$ ; here $\lambda_1$ is the largest part of the partition $\lambda$ .

Cite

@article{arxiv.1608.05043,
  title  = {On semiring complexity of Schur polynomials},
  author = {Sergey Fomin and Dima Grigoriev and Dorian Nogneng and Eric Schost},
  journal= {arXiv preprint arXiv:1608.05043},
  year   = {2018}
}

Comments

22 pages, final version, to appear in Computational Complexity. Section 4 rewritten per referee's suggestion, to make the argument more explicit

On semiring complexity of Schur polynomials

Abstract

Cite

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