Trapezoids and Deltoids in Wide Planar Point Sets
We call a set of n points in the Euclidean plane “wide” if at most n of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is Ω ( n 3 log n ) and O ( n 3 log 2 n ) while for deltoids we have Ω ( n 5 / 2 ) and O ( n 8 / 3 log n ) .
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| Veröffentlicht in: | Graphs and combinatorics 2019-05, Vol.35 (3), p.569-578 |
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| container_end_page | 578 |
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| container_issue | 3 |
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| container_title | Graphs and combinatorics |
| container_volume | 35 |
| creator | Elekes, Gy |
| description | We call a set of
n
points in the Euclidean plane “wide” if at most
n
of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is
Ω
(
n
3
log
n
)
and
O
(
n
3
log
2
n
)
while for deltoids we have
Ω
(
n
5
/
2
)
and
O
(
n
8
/
3
log
n
)
. |
| doi_str_mv | 10.1007/s00373-019-02009-2 |
| format | Article |
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n
points in the Euclidean plane “wide” if at most
n
of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is
Ω
(
n
3
log
n
)
and
O
(
n
3
log
2
n
)
while for deltoids we have
Ω
(
n
5
/
2
)
and
O
(
n
8
/
3
log
n
)
.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-019-02009-2</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Engineering Design ; Euclidean geometry ; Mathematics ; Mathematics and Statistics ; Original Paper ; Trapezoids</subject><ispartof>Graphs and combinatorics, 2019-05, Vol.35 (3), p.569-578</ispartof><rights>The Author(s) 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-7118c1f9639aa5a0336bbc9cf73a393f56cb79c10ddc94fcb980bff1d596892b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00373-019-02009-2$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-019-02009-2$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Elekes, Gy</creatorcontrib><title>Trapezoids and Deltoids in Wide Planar Point Sets</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>We call a set of
n
points in the Euclidean plane “wide” if at most
n
of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is
Ω
(
n
3
log
n
)
and
O
(
n
3
log
2
n
)
while for deltoids we have
Ω
(
n
5
/
2
)
and
O
(
n
8
/
3
log
n
)
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n
points in the Euclidean plane “wide” if at most
n
of its points are collinear. We show that in such sets, the maximum possible number of trapezoids is
Ω
(
n
3
log
n
)
and
O
(
n
3
log
2
n
)
while for deltoids we have
Ω
(
n
5
/
2
)
and
O
(
n
8
/
3
log
n
)
.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-019-02009-2</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0911-0119 |
| ispartof | Graphs and combinatorics, 2019-05, Vol.35 (3), p.569-578 |
| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_journals_2210053590 |
| source | Springer journals |
| subjects | Combinatorics Engineering Design Euclidean geometry Mathematics Mathematics and Statistics Original Paper Trapezoids |
| title | Trapezoids and Deltoids in Wide Planar Point Sets |
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