Permutation Totally Symmetric Self-Complementary Plane Partitions

Permutation Totally Symmetric Self-Complementary Plane Partitions

Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statis...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Annals of combinatorics 2018-09, Vol.22 (3), p.641-671
1. Verfasser: Striker, Jessica
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Economic models
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix methods
Partitions (mathematics)
Permutations
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 671
container_issue 3
container_start_page 641
container_title Annals of combinatorics
container_volume 22
creator Striker, Jessica
description Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permutations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations.
doi_str_mv 10.1007/s00026-018-0394-0
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2091267590</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2091267590</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-302208f7b3d4c730e1775d4b19dc94f49fa2f3528aed1ef3fe07c8c55ad267743</originalsourceid><addsrcrecordid>eNp1kE9LAzEQxYMoWKsfwNuC5-gk2d1sjqWoFQoWWs8hzU5ky_6pSXrotzfrCp48zYN5b-bxI-SewSMDkE8BAHhJgVUUhMopXJAZcKaoAJVf_ui0ASivyU0Ih6QkCD4jiw367hRNbIY-2w3RtO052567DqNvbLbF1tHl0B1b7LCPxp-zTWt6zDbGx2YMhVty5Uwb8O53zsnHy_NuuaLr99e35WJNrWBlTD04h8rJvahzKwUgk7Ko8z1TtVW5y5Uz3ImCVwZrhk44BGkrWxSm5qWUuZiTh-nu0Q9fJwxRH4aT79NLzUGxZCoUJBebXNYPIXh0-uibLvXWDPRISk-kdCKlR1J6zPApE5K3_0T_d_n_0DeiF2sm</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2091267590</pqid></control><display><type>article</type><title>Permutation Totally Symmetric Self-Complementary Plane Partitions</title><source>Springer Nature - Complete Springer Journals</source><creator>Striker, Jessica</creator><creatorcontrib>Striker, Jessica</creatorcontrib><description>Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permutations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations.</description><identifier>ISSN: 0218-0006</identifier><identifier>EISSN: 0219-3094</identifier><identifier>DOI: 10.1007/s00026-018-0394-0</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Combinatorics ; Economic models ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Matrix methods ; Partitions (mathematics) ; Permutations</subject><ispartof>Annals of combinatorics, 2018-09, Vol.22 (3), p.641-671</ispartof><rights>Springer International Publishing AG, part of Springer Nature 2018</rights><rights>Copyright Springer Science &amp; Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-302208f7b3d4c730e1775d4b19dc94f49fa2f3528aed1ef3fe07c8c55ad267743</citedby><cites>FETCH-LOGICAL-c316t-302208f7b3d4c730e1775d4b19dc94f49fa2f3528aed1ef3fe07c8c55ad267743</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/s00026-018-0394-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00026-018-0394-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Striker, Jessica</creatorcontrib><title>Permutation Totally Symmetric Self-Complementary Plane Partitions</title><title>Annals of combinatorics</title><addtitle>Ann. Comb</addtitle><description>Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permutations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations.</description><subject>Combinatorics</subject><subject>Economic models</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix methods</subject><subject>Partitions (mathematics)</subject><subject>Permutations</subject><issn>0218-0006</issn><issn>0219-3094</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE9LAzEQxYMoWKsfwNuC5-gk2d1sjqWoFQoWWs8hzU5ky_6pSXrotzfrCp48zYN5b-bxI-SewSMDkE8BAHhJgVUUhMopXJAZcKaoAJVf_ui0ASivyU0Ih6QkCD4jiw367hRNbIY-2w3RtO052567DqNvbLbF1tHl0B1b7LCPxp-zTWt6zDbGx2YMhVty5Uwb8O53zsnHy_NuuaLr99e35WJNrWBlTD04h8rJvahzKwUgk7Ko8z1TtVW5y5Uz3ImCVwZrhk44BGkrWxSm5qWUuZiTh-nu0Q9fJwxRH4aT79NLzUGxZCoUJBebXNYPIXh0-uibLvXWDPRISk-kdCKlR1J6zPApE5K3_0T_d_n_0DeiF2sm</recordid><startdate>20180901</startdate><enddate>20180901</enddate><creator>Striker, Jessica</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180901</creationdate><title>Permutation Totally Symmetric Self-Complementary Plane Partitions</title><author>Striker, Jessica</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-302208f7b3d4c730e1775d4b19dc94f49fa2f3528aed1ef3fe07c8c55ad267743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Combinatorics</topic><topic>Economic models</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix methods</topic><topic>Partitions (mathematics)</topic><topic>Permutations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Striker, Jessica</creatorcontrib><collection>CrossRef</collection><jtitle>Annals of combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Striker, Jessica</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Permutation Totally Symmetric Self-Complementary Plane Partitions</atitle><jtitle>Annals of combinatorics</jtitle><stitle>Ann. Comb</stitle><date>2018-09-01</date><risdate>2018</risdate><volume>22</volume><issue>3</issue><spage>641</spage><epage>671</epage><pages>641-671</pages><issn>0218-0006</issn><eissn>0219-3094</eissn><abstract>Alternating sign matrices and totally symmetric self-complementary plane partitions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permutations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00026-018-0394-0</doi><tpages>31</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0218-0006
ispartof Annals of combinatorics, 2018-09, Vol.22 (3), p.641-671
issn 0218-0006
0219-3094
language eng
recordid cdi_proquest_journals_2091267590
source Springer Nature - Complete Springer Journals
subjects Combinatorics
Economic models
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix methods
Partitions (mathematics)
Permutations
title Permutation Totally Symmetric Self-Complementary Plane Partitions
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T11%3A40%3A36IST&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=Permutation%20Totally%20Symmetric%20Self-Complementary%20Plane%20Partitions&rft.jtitle=Annals%20of%20combinatorics&rft.au=Striker,%20Jessica&rft.date=2018-09-01&rft.volume=22&rft.issue=3&rft.spage=641&rft.epage=671&rft.pages=641-671&rft.issn=0218-0006&rft.eissn=0219-3094&rft_id=info:doi/10.1007/s00026-018-0394-0&rft_dat=%3Cproquest_cross%3E2091267590%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=2091267590&rft_id=info:pmid/&rfr_iscdi=true