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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Veröffentlicht in:Computational complexity Jg. 27; H. 4; S. 595 - 616
Hauptverfasser: Fomin, Sergey, Grigoriev, Dima, Nogneng, Dorian, Schost, Éric
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2018
Springer Nature B.V
Springer Verlag
Schlagworte:
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-Zugang:Volltext
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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content type line 14
ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-018-0169-3