Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley. / Gesmundo, Fulvio; Landsberg, Joseph M.

I: Theory of Computing, Bind 15, 3, 2019.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Gesmundo, F & Landsberg, JM 2019, 'Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley', Theory of Computing, bind 15, 3. https://doi.org/10.4086/toc.2019.v015a003

APA

Gesmundo, F., & Landsberg, J. M. (2019). Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley. Theory of Computing, 15, [3]. https://doi.org/10.4086/toc.2019.v015a003

Vancouver

Gesmundo F, Landsberg JM. Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley. Theory of Computing. 2019;15. 3. https://doi.org/10.4086/toc.2019.v015a003

Author

Gesmundo, Fulvio ; Landsberg, Joseph M. / Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley. I: Theory of Computing. 2019 ; Bind 15.

Bibtex

@article{7006be565eeb4300b681e043a79bfd0c,
title = "Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley",
abstract = "We answer a question of K. Mulmuley. Efremenko et al. (Math. Comp., 2018) have shown that the method of shifted partial derivatives cannot be used to separate the padded permanent from the determinant. Mulmuley asked if this “no-go” result could be extended to a model without padding. We prove this is indeed the case using the iterated matrix multiplication polynomial. We also provide several examples of polynomials with maximal space of partial derivatives, including the complete symmetric polynomials. We apply Koszul flattenings to these polynomials to have the first explicit sequence of polynomials with symmetric border rank lower bounds higher than the bounds attainable via partial derivatives. ",
author = "Fulvio Gesmundo and Landsberg, {Joseph M.}",
year = "2019",
doi = "10.4086/toc.2019.v015a003",
language = "English",
volume = "15",
journal = "Theory of Computing",
issn = "1557-2862",
publisher = "University of Chicago, Department of Computer Science",

}

RIS

TY - JOUR

T1 - Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley

AU - Gesmundo, Fulvio

AU - Landsberg, Joseph M.

PY - 2019

Y1 - 2019

N2 - We answer a question of K. Mulmuley. Efremenko et al. (Math. Comp., 2018) have shown that the method of shifted partial derivatives cannot be used to separate the padded permanent from the determinant. Mulmuley asked if this “no-go” result could be extended to a model without padding. We prove this is indeed the case using the iterated matrix multiplication polynomial. We also provide several examples of polynomials with maximal space of partial derivatives, including the complete symmetric polynomials. We apply Koszul flattenings to these polynomials to have the first explicit sequence of polynomials with symmetric border rank lower bounds higher than the bounds attainable via partial derivatives.

AB - We answer a question of K. Mulmuley. Efremenko et al. (Math. Comp., 2018) have shown that the method of shifted partial derivatives cannot be used to separate the padded permanent from the determinant. Mulmuley asked if this “no-go” result could be extended to a model without padding. We prove this is indeed the case using the iterated matrix multiplication polynomial. We also provide several examples of polynomials with maximal space of partial derivatives, including the complete symmetric polynomials. We apply Koszul flattenings to these polynomials to have the first explicit sequence of polynomials with symmetric border rank lower bounds higher than the bounds attainable via partial derivatives.

U2 - 10.4086/toc.2019.v015a003

DO - 10.4086/toc.2019.v015a003

M3 - Journal article

VL - 15

JO - Theory of Computing

JF - Theory of Computing

SN - 1557-2862

M1 - 3

ER -

ID: 231712793