On read-k projections of the determinant

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00618207" target="_blank" >RIV/67985840:_____/25:00618207 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.STACS.2025.53" target="_blank" >https://doi.org/10.4230/LIPIcs.STACS.2025.53</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2025.53" target="_blank" >10.4230/LIPIcs.STACS.2025.53</a>

Result language

angličtina

Original language name

On read-k projections of the determinant

Original language description

We consider read-k determinantal representations of polynomials and prove some non-expressibility results. A square matrix M whose entries are variables or field elements will be called read-k, if every variable occurs at most k times in M. It will be called a determinantal representation of a polynomial f if f = det(M). We show that the n × n permanent polynomial does not have a read-k determinantal representation for k ∈ o(√n/log n) (over a field of characteristic different from two). We also obtain a quantitative strengthening of this result by giving a similar non-expressibility for k ∈ o(√n/log n) for an explicit n-variate multilinear polynomial (as opposed to the permanent which is n2-variate).

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GA25-16311S" target="_blank" >GA25-16311S: Complexity of computation, communication, and search</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

ISBN

978-3-95977-365-2

ISSN

1868-8969

e-ISSN

—

Number of pages

7

Pages from-to

53

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Jena

Event date

Mar 4, 2025

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

001532683200053