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 λ ( x 1 , ⋯ , x k ) labeled by a partition λ = ( λ 1 ≥ λ 2 ≥ ⋯ ) is bounded by O ( log ( λ 1 ) ) provided the num...

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Bibliographic Details
Published in:Computational complexity Vol. 27; no. 4; pp. 595 - 616
Main Authors: Fomin, Sergey, Grigoriev, Dima, Nogneng, Dorian, Schost, Éric
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2018
Springer Nature B.V
Springer Verlag
Subjects:
Algorithm Analysis and Problem Complexity
Complexity
Computational Mathematics and Numerical Analysis
Computer Science
Mathematical analysis
Mathematics
Polynomials
Primary 68Q25
Secondary 05E05
Semiring complexity
Schur function
Young tableaux
ISSN:1016-3328, 1420-8954
Online Access:Get full text
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Summary: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 λ ( x 1 , ⋯ , x k ) labeled by a partition λ = ( λ 1 ≥ λ 2 ≥ ⋯ ) is bounded by O ( log ( λ 1 ) ) provided the number of variables k is fixed.
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ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-018-0169-3