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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Vydáno v:Computational complexity Ročník 27; číslo 4; s. 595 - 616
Hlavní autoři: Fomin, Sergey, Grigoriev, Dima, Nogneng, Dorian, Schost, Éric
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.12.2018
Springer Nature B.V
Springer Verlag
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1016-3328
1420-8954
DOI:10.1007/s00037-018-0169-3