A New Lower Bound Based on Gromov's Method of Selecting Heavily Covered Points

KRÁĽ, Daniel; L MACH a JS SERENI. A New Lower Bound Based on Gromov's Method of Selecting Heavily Covered Points. DISCRETE & COMPUTATIONAL GEOMETRY. NEW YORK: SPRINGER, 2012, roč. 48, č. 2, s. 487-498. ISSN 0179-5376. Dostupné z: https://doi.org/10.1007/s00454-012-9419-3.

Základní údaje

Originální název

A New Lower Bound Based on Gromov's Method of Selecting Heavily Covered Points

Autoři

KRÁĽ, Daniel; L MACH a JS SERENI

Vydání

DISCRETE & COMPUTATIONAL GEOMETRY, NEW YORK, SPRINGER, 2012, 0179-5376

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Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Utajení

není předmětem státního či obchodního tajemství

Impakt faktor

Impact factor: 0.649

Označené pro přenos do RIV

Ne

DOI

https://doi.org/10.1007/s00454-012-9419-3

UT WoS

000306432400012

Klíčová slova anglicky

Flag algebras; Covering points by simplicies; Cofilling profiles; Boros-Furedi-Barany-Pach-Gromov theorem

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Anotace

V originále

Boros and Furedi (for d=2) and Barany (for arbitrary d) proved that there exists a positive real number c (d) such that for every set P of n points in R (d) in general position, there exists a point of R (d) contained in at least d-simplices with vertices at the points of P. Gromov improved the known lower bound on c (d) by topological means. Using methods from extremal combinatorics, we improve one of the quantities appearing in Gromov's approach and thereby provide a new stronger lower bound on c (d) for arbitrary d. In particular, we improve the lower bound on c (3) from 0.06332 to more than 0.07480; the best upper bound known on c (3) being 0.09375.