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Packing tripods: Narrowing the density gap. / Tiskin, Alexander.

в: Discrete Mathematics, Том 307, № 16, 28.07.2007, стр. 1973-1981.

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Harvard

Tiskin, A 2007, 'Packing tripods: Narrowing the density gap', Discrete Mathematics, Том. 307, № 16, стр. 1973-1981. https://doi.org/10.1016/j.disc.2004.12.028

APA

Tiskin, A. (2007). Packing tripods: Narrowing the density gap. Discrete Mathematics, 307(16), 1973-1981. https://doi.org/10.1016/j.disc.2004.12.028

Vancouver

Tiskin A. Packing tripods: Narrowing the density gap. Discrete Mathematics. 2007 Июль 28;307(16):1973-1981. https://doi.org/10.1016/j.disc.2004.12.028

Author

Tiskin, Alexander. / Packing tripods: Narrowing the density gap. в: Discrete Mathematics. 2007 ; Том 307, № 16. стр. 1973-1981.

BibTeX

@article{98bac8f071ab4af1bd5ddb2ffb5ae006,
title = "Packing tripods: Narrowing the density gap",
abstract = "In 1984, Stein and his co-authors posed a problem concerning simple three-dimensional shapes, known as semicrosses, or tripods. By definition, a tripod of order n is formed by a corner and the three adjacent edges of an integer n × n × n cube. How densely can one fill the space with non-overlapping tripods of a given order? In particular, is it possible to fill a constant fraction of the space as tripod order tends to infinity? In this paper, we settle the second question in the negative: the fraction of the space that can be filled with tripods must be infinitely small as the order grows. We also make a step towards the solution of the first question, by improving the currently known asymptotic lower bound on tripod packing density, and by presenting some computational results on low-order packings. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",
keywords = "Regularity lemma, Semicross packing, Tripod packing",
author = "Alexander Tiskin",
year = "2007",
month = jul,
day = "28",
doi = "10.1016/j.disc.2004.12.028",
language = "English",
volume = "307",
pages = "1973--1981",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "16",

}

RIS

TY - JOUR

T1 - Packing tripods: Narrowing the density gap

AU - Tiskin, Alexander

PY - 2007/7/28

Y1 - 2007/7/28

N2 - In 1984, Stein and his co-authors posed a problem concerning simple three-dimensional shapes, known as semicrosses, or tripods. By definition, a tripod of order n is formed by a corner and the three adjacent edges of an integer n × n × n cube. How densely can one fill the space with non-overlapping tripods of a given order? In particular, is it possible to fill a constant fraction of the space as tripod order tends to infinity? In this paper, we settle the second question in the negative: the fraction of the space that can be filled with tripods must be infinitely small as the order grows. We also make a step towards the solution of the first question, by improving the currently known asymptotic lower bound on tripod packing density, and by presenting some computational results on low-order packings. © 2006 Elsevier B.V. All rights reserved.

AB - In 1984, Stein and his co-authors posed a problem concerning simple three-dimensional shapes, known as semicrosses, or tripods. By definition, a tripod of order n is formed by a corner and the three adjacent edges of an integer n × n × n cube. How densely can one fill the space with non-overlapping tripods of a given order? In particular, is it possible to fill a constant fraction of the space as tripod order tends to infinity? In this paper, we settle the second question in the negative: the fraction of the space that can be filled with tripods must be infinitely small as the order grows. We also make a step towards the solution of the first question, by improving the currently known asymptotic lower bound on tripod packing density, and by presenting some computational results on low-order packings. © 2006 Elsevier B.V. All rights reserved.

KW - Regularity lemma

KW - Semicross packing

KW - Tripod packing

UR - http://www.scopus.com/inward/record.url?scp=34248651541&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2004.12.028

DO - 10.1016/j.disc.2004.12.028

M3 - Article

AN - SCOPUS:34248651541

VL - 307

SP - 1973

EP - 1981

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 16

ER -

ID: 127711126