# 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

, Volume 27 (4) – Jun 4, 2018
22 pages

/lp/springer_journal/on-semiring-complexity-of-schur-polynomials-8X8qRqu9lR
Publisher
Springer Journals
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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations