On semiring complexity of Schur polynomials

On semiring complexity of Schur polynomials 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 $${s_\lambda(x_1,\dots,x_k)}$$ s λ ( x 1 , ⋯ , x k ) labeled by a partition $${\lambda=(\lambda_1\ge\lambda_2\ge\cdots)}$$ λ = ( λ 1 ≥ λ 2 ≥ ⋯ ) is bounded by $${O(\log(\lambda_1))}$$ O ( log ( λ 1 ) ) provided the number of variables k is fixed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Complexity Springer Journals

On semiring complexity of Schur polynomials

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Computational Mathematics and Numerical Analysis
ISSN
1016-3328
eISSN
1420-8954
D.O.I.
10.1007/s00037-018-0169-3
Publisher site
See Article on Publisher Site

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 $${s_\lambda(x_1,\dots,x_k)}$$ s λ ( x 1 , ⋯ , x k ) labeled by a partition $${\lambda=(\lambda_1\ge\lambda_2\ge\cdots)}$$ λ = ( λ 1 ≥ λ 2 ≥ ⋯ ) is bounded by $${O(\log(\lambda_1))}$$ O ( log ( λ 1 ) ) provided the number of variables k is fixed.

Journal

Computational ComplexitySpringer Journals

Published: Jun 4, 2018

References

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