Sós Permutations
Let for fixed real parameters α and β. For any positive integer n, define the Sós permutation π to be the lexicographically first permutation such that . In this article, we give a bijection between Sós permutations and regions in a partition of the parameter space . This allows us to enumerate thes...
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| Veröffentlicht in: | The American mathematical monthly 2021-05, Vol.128 (5), p.407-422 |
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| container_issue | 5 |
| container_start_page | 407 |
| container_title | The American mathematical monthly |
| container_volume | 128 |
| creator | Bockting-Conrad, Sarah Kashina, Yevgenia Petersen, T. Kyle Tenner, Bridget Eileen |
| description | Let
for fixed real parameters α and β. For any positive integer n, define the Sós permutation π to be the lexicographically first permutation such that
. In this article, we give a bijection between Sós permutations and regions in a partition of the parameter space
. This allows us to enumerate these permutations and to obtain the following "three areas" theorem: in any vertical strip
, with
a Farey interval, there are at most three distinct areas of regions, and one of these areas is the sum of the other two. |
| doi_str_mv | 10.1080/00029890.2021.1889911 |
| format | Article |
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for fixed real parameters α and β. For any positive integer n, define the Sós permutation π to be the lexicographically first permutation such that
. In this article, we give a bijection between Sós permutations and regions in a partition of the parameter space
. This allows us to enumerate these permutations and to obtain the following "three areas" theorem: in any vertical strip
, with
a Farey interval, there are at most three distinct areas of regions, and one of these areas is the sum of the other two.</description><identifier>ISSN: 0002-9890</identifier><identifier>EISSN: 1930-0972</identifier><identifier>DOI: 10.1080/00029890.2021.1889911</identifier><language>eng</language><publisher>Washington: Taylor & Francis</publisher><subject>Integer programming ; Parameter optimization ; Parameters ; Permutations ; Primary 05A05 ; Secondary 11K06 ; Theorems ; Variables</subject><ispartof>The American mathematical monthly, 2021-05, Vol.128 (5), p.407-422</ispartof><rights>THE MATHEMATICAL ASSOCIATION OF AMERICA</rights><rights>Copyright Taylor & Francis Ltd. May 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c308t-2b3b4d319b50377c5a2019b96ef008675885f0298c7563d9442b351edf765eb23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Bockting-Conrad, Sarah</creatorcontrib><creatorcontrib>Kashina, Yevgenia</creatorcontrib><creatorcontrib>Petersen, T. Kyle</creatorcontrib><creatorcontrib>Tenner, Bridget Eileen</creatorcontrib><title>Sós Permutations</title><title>The American mathematical monthly</title><description>Let
for fixed real parameters α and β. For any positive integer n, define the Sós permutation π to be the lexicographically first permutation such that
. In this article, we give a bijection between Sós permutations and regions in a partition of the parameter space
. This allows us to enumerate these permutations and to obtain the following "three areas" theorem: in any vertical strip
, with
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for fixed real parameters α and β. For any positive integer n, define the Sós permutation π to be the lexicographically first permutation such that
. In this article, we give a bijection between Sós permutations and regions in a partition of the parameter space
. This allows us to enumerate these permutations and to obtain the following "three areas" theorem: in any vertical strip
, with
a Farey interval, there are at most three distinct areas of regions, and one of these areas is the sum of the other two.</abstract><cop>Washington</cop><pub>Taylor & Francis</pub><doi>10.1080/00029890.2021.1889911</doi><tpages>16</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9890 |
| ispartof | The American mathematical monthly, 2021-05, Vol.128 (5), p.407-422 |
| issn | 0002-9890 1930-0972 |
| language | eng |
| recordid | cdi_crossref_primary_10_1080_00029890_2021_1889911 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | Integer programming Parameter optimization Parameters Permutations Primary 05A05 Secondary 11K06 Theorems Variables |
| title | Sós Permutations |
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