Geometrical Bijections in Discrete Lattices
We define uniformly spread sets as point sets in d-dimensional Euclidean space that are wobbling equivalent to the standard lattice ℤd. A linear image ϕ(ℤd) of ℤd is shown to be uniformly spread if and only if det(ϕ) = 1. Explicit geometrical and number-theoretical constructions are given. In 2-dime...
Gespeichert in:
| Veröffentlicht in: | Combinatorics, probability & computing probability & computing, 1999-01, Vol.8 (1-2), p.109-129 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 129 |
|---|---|
| container_issue | 1-2 |
| container_start_page | 109 |
| container_title | Combinatorics, probability & computing |
| container_volume | 8 |
| creator | CARSTENS, HANS-GEORG DEUBER, WALTER A. THUMSER, WOLFGANG KOPPENRADE, ELKE |
| description | We define uniformly spread sets as point sets in d-dimensional
Euclidean space that are wobbling equivalent to the standard lattice
ℤd. A linear image ϕ(ℤd)
of ℤd is shown
to be uniformly spread if and only if det(ϕ) = 1. Explicit geometrical and number-theoretical constructions are given. In 2-dimensional Euclidean space we obtain bounds
for the wobbling distance for rotations, shearings and stretchings that are close to optimal.
Our methods also allow us to analyse the discrepancy of certain billiards. Finally, we take a
look at paradoxical situations and exhibit recursive point sets that are wobbling equivalent,
but not recursively so. |
| doi_str_mv | 10.1017/S0963548398003484 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_203983868</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0963548398003484</cupid><sourcerecordid>1397687941</sourcerecordid><originalsourceid>FETCH-LOGICAL-c352t-58295a45adc35e26e6f8b65c2a0b45dbd0093798ab2ce01ddf679c14c4e7b55d3</originalsourceid><addsrcrecordid>eNp1UMtOwzAQtBBIlMIHcIu4osA6fsQ5QoEGiECIwtVynA1yaZtiuxL8PalawQFxWq1mZmd2CDmmcEaB5ufPUEgmuGKFAmBc8R0yoFwWaUYl2yWDNZyu8X1yEMIUAISQMCCnY-zmGL2zZpZcuina6LpFSNwiuXLBeoyYVCZGZzEckr3WzAIebeeQvNxcT0ZlWj2Ob0cXVWqZyGIqVFYIw4Vp-h0zibJVtRQ2M1Bz0dQNQMHyQpk6swi0aVqZF5ZyyzGvhWjYkJxs7i5997HCEPW0W_lFb6kz6B9kSqqeRDck67sQPLZ66d3c-C9NQa8r0X8q6TXpRuNCxM8fgfHvWuYsF1qOn_Rd9fpQ3kOpJz2fbT3MvPauecPfJP-7fAOc4XDi</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>203983868</pqid></control><display><type>article</type><title>Geometrical Bijections in Discrete Lattices</title><source>Cambridge University Press Journals Complete</source><creator>CARSTENS, HANS-GEORG ; DEUBER, WALTER A. ; THUMSER, WOLFGANG ; KOPPENRADE, ELKE</creator><creatorcontrib>CARSTENS, HANS-GEORG ; DEUBER, WALTER A. ; THUMSER, WOLFGANG ; KOPPENRADE, ELKE</creatorcontrib><description>We define uniformly spread sets as point sets in d-dimensional
Euclidean space that are wobbling equivalent to the standard lattice
ℤd. A linear image ϕ(ℤd)
of ℤd is shown
to be uniformly spread if and only if det(ϕ) = 1. Explicit geometrical and number-theoretical constructions are given. In 2-dimensional Euclidean space we obtain bounds
for the wobbling distance for rotations, shearings and stretchings that are close to optimal.
Our methods also allow us to analyse the discrepancy of certain billiards. Finally, we take a
look at paradoxical situations and exhibit recursive point sets that are wobbling equivalent,
but not recursively so.</description><identifier>ISSN: 0963-5483</identifier><identifier>EISSN: 1469-2163</identifier><identifier>DOI: 10.1017/S0963548398003484</identifier><language>eng</language><publisher>Cambridge: Cambridge University Press</publisher><ispartof>Combinatorics, probability & computing, 1999-01, Vol.8 (1-2), p.109-129</ispartof><rights>1999 Cambridge University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c352t-58295a45adc35e26e6f8b65c2a0b45dbd0093798ab2ce01ddf679c14c4e7b55d3</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0963548398003484/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,776,780,27901,27902,55603</link.rule.ids></links><search><creatorcontrib>CARSTENS, HANS-GEORG</creatorcontrib><creatorcontrib>DEUBER, WALTER A.</creatorcontrib><creatorcontrib>THUMSER, WOLFGANG</creatorcontrib><creatorcontrib>KOPPENRADE, ELKE</creatorcontrib><title>Geometrical Bijections in Discrete Lattices</title><title>Combinatorics, probability & computing</title><addtitle>Combinator. Probab. Comp</addtitle><description>We define uniformly spread sets as point sets in d-dimensional
Euclidean space that are wobbling equivalent to the standard lattice
ℤd. A linear image ϕ(ℤd)
of ℤd is shown
to be uniformly spread if and only if det(ϕ) = 1. Explicit geometrical and number-theoretical constructions are given. In 2-dimensional Euclidean space we obtain bounds
for the wobbling distance for rotations, shearings and stretchings that are close to optimal.
Our methods also allow us to analyse the discrepancy of certain billiards. Finally, we take a
look at paradoxical situations and exhibit recursive point sets that are wobbling equivalent,
but not recursively so.</description><issn>0963-5483</issn><issn>1469-2163</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNp1UMtOwzAQtBBIlMIHcIu4osA6fsQ5QoEGiECIwtVynA1yaZtiuxL8PalawQFxWq1mZmd2CDmmcEaB5ufPUEgmuGKFAmBc8R0yoFwWaUYl2yWDNZyu8X1yEMIUAISQMCCnY-zmGL2zZpZcuina6LpFSNwiuXLBeoyYVCZGZzEckr3WzAIebeeQvNxcT0ZlWj2Ob0cXVWqZyGIqVFYIw4Vp-h0zibJVtRQ2M1Bz0dQNQMHyQpk6swi0aVqZF5ZyyzGvhWjYkJxs7i5997HCEPW0W_lFb6kz6B9kSqqeRDck67sQPLZ66d3c-C9NQa8r0X8q6TXpRuNCxM8fgfHvWuYsF1qOn_Rd9fpQ3kOpJz2fbT3MvPauecPfJP-7fAOc4XDi</recordid><startdate>199901</startdate><enddate>199901</enddate><creator>CARSTENS, HANS-GEORG</creator><creator>DEUBER, WALTER A.</creator><creator>THUMSER, WOLFGANG</creator><creator>KOPPENRADE, ELKE</creator><general>Cambridge University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>199901</creationdate><title>Geometrical Bijections in Discrete Lattices</title><author>CARSTENS, HANS-GEORG ; DEUBER, WALTER A. ; THUMSER, WOLFGANG ; KOPPENRADE, ELKE</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c352t-58295a45adc35e26e6f8b65c2a0b45dbd0093798ab2ce01ddf679c14c4e7b55d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>CARSTENS, HANS-GEORG</creatorcontrib><creatorcontrib>DEUBER, WALTER A.</creatorcontrib><creatorcontrib>THUMSER, WOLFGANG</creatorcontrib><creatorcontrib>KOPPENRADE, ELKE</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Combinatorics, probability & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CARSTENS, HANS-GEORG</au><au>DEUBER, WALTER A.</au><au>THUMSER, WOLFGANG</au><au>KOPPENRADE, ELKE</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Geometrical Bijections in Discrete Lattices</atitle><jtitle>Combinatorics, probability & computing</jtitle><addtitle>Combinator. Probab. Comp</addtitle><date>1999-01</date><risdate>1999</risdate><volume>8</volume><issue>1-2</issue><spage>109</spage><epage>129</epage><pages>109-129</pages><issn>0963-5483</issn><eissn>1469-2163</eissn><abstract>We define uniformly spread sets as point sets in d-dimensional
Euclidean space that are wobbling equivalent to the standard lattice
ℤd. A linear image ϕ(ℤd)
of ℤd is shown
to be uniformly spread if and only if det(ϕ) = 1. Explicit geometrical and number-theoretical constructions are given. In 2-dimensional Euclidean space we obtain bounds
for the wobbling distance for rotations, shearings and stretchings that are close to optimal.
Our methods also allow us to analyse the discrepancy of certain billiards. Finally, we take a
look at paradoxical situations and exhibit recursive point sets that are wobbling equivalent,
but not recursively so.</abstract><cop>Cambridge</cop><pub>Cambridge University Press</pub><doi>10.1017/S0963548398003484</doi><tpages>21</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0963-5483 |
| ispartof | Combinatorics, probability & computing, 1999-01, Vol.8 (1-2), p.109-129 |
| issn | 0963-5483 1469-2163 |
| language | eng |
| recordid | cdi_proquest_journals_203983868 |
| source | Cambridge University Press Journals Complete |
| title | Geometrical Bijections in Discrete Lattices |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-15T08%3A50%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Geometrical%20Bijections%20in%20Discrete%20Lattices&rft.jtitle=Combinatorics,%20probability%20&%20computing&rft.au=CARSTENS,%20HANS-GEORG&rft.date=1999-01&rft.volume=8&rft.issue=1-2&rft.spage=109&rft.epage=129&rft.pages=109-129&rft.issn=0963-5483&rft.eissn=1469-2163&rft_id=info:doi/10.1017/S0963548398003484&rft_dat=%3Cproquest_cross%3E1397687941%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=203983868&rft_id=info:pmid/&rft_cupid=10_1017_S0963548398003484&rfr_iscdi=true |