Loading…
Descents of $\lambda$-unimodal cyclic permutations
We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combi...
Saved in:
| Published in: | Discrete mathematics and theoretical computer science 2014-01, Vol.DMTCS Proceedings vol. AT,... (Proceedings), p.417-428 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | |
|---|---|
| cites | |
| container_end_page | 428 |
| container_issue | Proceedings |
| container_start_page | 417 |
| container_title | Discrete mathematics and theoretical computer science |
| container_volume | DMTCS Proceedings vol. AT,... |
| creator | Archer, Kassie |
| description | We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.
Nous prouvons une identité conjecturée par Adin et Roichman impliquant les ensembles des descentes des permutations cycliques $\lambda$-unimodales. Ces permutations apparaissent dans les formules des caractères pour certaines représentations du groupe symétrique, et ces formules sont généralement prouvées dans une manière algébrique. Ici, nous donnons une preuve combinatoire pour une telle formule et discutons les conséquences pour la distribution de l’ensemble des descentes sur des permutations cycliques. |
| doi_str_mv | 10.46298/dmtcs.2411 |
| format | article |
| fullrecord | <record><control><sourceid>hal_doaj_</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_f0faef00a8134169952174ee863a5fdb</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_f0faef00a8134169952174ee863a5fdb</doaj_id><sourcerecordid>oai_HAL_hal_01207601v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c1361-b2bbff643a4d990e0ff5ae26e8e933f54d54215598466ac664cb252f95dc01513</originalsourceid><addsrcrecordid>eNpVkMtKA0EQRRtRMEZX_sAsshGZWP3M9DLER4SAG90JTU0_dMJMOnRPhPy9eYjoqopL1blwCLmmMBaK6erOdb3NYyYoPSEDypUsK5Bw-mc_Jxc5LwEo02IyIOzeZ-tXfS5iKEbvLXa1w1G5WTVddNgWdmvbxhZrn7pNj30TV_mSnAVss7_6mUPy9vjwOpuXi5en59l0UdpdGS1rVtchKMFROK3BQwgSPVO-8przIIWTglEpdSWUQquUsDWTLGjpLFBJ-ZA8H7ku4tKsU9Nh2pqIjTkEMX0YTH1jW28CBPQBACvKBVVaS0YnwvtKcZTB1TvWzZH1ie0_1Hy6MPts5wMmCujXvvf2eGtTzDn58PtAwRw0m4Nms9fMvwFXMG6B</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Descents of $\lambda$-unimodal cyclic permutations</title><source>Publicly Available Content Database</source><creator>Archer, Kassie</creator><creatorcontrib>Archer, Kassie</creatorcontrib><description>We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.
Nous prouvons une identité conjecturée par Adin et Roichman impliquant les ensembles des descentes des permutations cycliques $\lambda$-unimodales. Ces permutations apparaissent dans les formules des caractères pour certaines représentations du groupe symétrique, et ces formules sont généralement prouvées dans une manière algébrique. Ici, nous donnons une preuve combinatoire pour une telle formule et discutons les conséquences pour la distribution de l’ensemble des descentes sur des permutations cycliques.</description><identifier>ISSN: 1365-8050</identifier><identifier>ISSN: 1462-7264</identifier><identifier>EISSN: 1365-8050</identifier><identifier>DOI: 10.46298/dmtcs.2411</identifier><language>eng</language><publisher>DMTCS</publisher><subject>[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] ; [math.math-co] mathematics [math]/combinatorics [math.co] ; characters of representations of the symmetric group ; Combinatorics ; Computer Science ; cyclic permutation ; descent ; Discrete Mathematics ; Mathematics ; necklaces</subject><ispartof>Discrete mathematics and theoretical computer science, 2014-01, Vol.DMTCS Proceedings vol. AT,... (Proceedings), p.417-428</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,309,310,314,780,784,789,790,885,23930,23931,25140,27924,27925</link.rule.ids><backlink>$$Uhttps://inria.hal.science/hal-01207601$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Archer, Kassie</creatorcontrib><title>Descents of $\lambda$-unimodal cyclic permutations</title><title>Discrete mathematics and theoretical computer science</title><description>We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.
Nous prouvons une identité conjecturée par Adin et Roichman impliquant les ensembles des descentes des permutations cycliques $\lambda$-unimodales. Ces permutations apparaissent dans les formules des caractères pour certaines représentations du groupe symétrique, et ces formules sont généralement prouvées dans une manière algébrique. Ici, nous donnons une preuve combinatoire pour une telle formule et discutons les conséquences pour la distribution de l’ensemble des descentes sur des permutations cycliques.</description><subject>[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]</subject><subject>[math.math-co] mathematics [math]/combinatorics [math.co]</subject><subject>characters of representations of the symmetric group</subject><subject>Combinatorics</subject><subject>Computer Science</subject><subject>cyclic permutation</subject><subject>descent</subject><subject>Discrete Mathematics</subject><subject>Mathematics</subject><subject>necklaces</subject><issn>1365-8050</issn><issn>1462-7264</issn><issn>1365-8050</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>DOA</sourceid><recordid>eNpVkMtKA0EQRRtRMEZX_sAsshGZWP3M9DLER4SAG90JTU0_dMJMOnRPhPy9eYjoqopL1blwCLmmMBaK6erOdb3NYyYoPSEDypUsK5Bw-mc_Jxc5LwEo02IyIOzeZ-tXfS5iKEbvLXa1w1G5WTVddNgWdmvbxhZrn7pNj30TV_mSnAVss7_6mUPy9vjwOpuXi5en59l0UdpdGS1rVtchKMFROK3BQwgSPVO-8przIIWTglEpdSWUQquUsDWTLGjpLFBJ-ZA8H7ku4tKsU9Nh2pqIjTkEMX0YTH1jW28CBPQBACvKBVVaS0YnwvtKcZTB1TvWzZH1ie0_1Hy6MPts5wMmCujXvvf2eGtTzDn58PtAwRw0m4Nms9fMvwFXMG6B</recordid><startdate>20140101</startdate><enddate>20140101</enddate><creator>Archer, Kassie</creator><general>DMTCS</general><general>Discrete Mathematics and Theoretical Computer Science</general><general>Discrete Mathematics & Theoretical Computer Science</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><scope>DOA</scope></search><sort><creationdate>20140101</creationdate><title>Descents of $\lambda$-unimodal cyclic permutations</title><author>Archer, Kassie</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1361-b2bbff643a4d990e0ff5ae26e8e933f54d54215598466ac664cb252f95dc01513</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]</topic><topic>[math.math-co] mathematics [math]/combinatorics [math.co]</topic><topic>characters of representations of the symmetric group</topic><topic>Combinatorics</topic><topic>Computer Science</topic><topic>cyclic permutation</topic><topic>descent</topic><topic>Discrete Mathematics</topic><topic>Mathematics</topic><topic>necklaces</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Archer, Kassie</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><collection>Open Access: DOAJ - Directory of Open Access Journals</collection><jtitle>Discrete mathematics and theoretical computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Archer, Kassie</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Descents of $\lambda$-unimodal cyclic permutations</atitle><jtitle>Discrete mathematics and theoretical computer science</jtitle><date>2014-01-01</date><risdate>2014</risdate><volume>DMTCS Proceedings vol. AT,...</volume><issue>Proceedings</issue><spage>417</spage><epage>428</epage><pages>417-428</pages><issn>1365-8050</issn><issn>1462-7264</issn><eissn>1365-8050</eissn><abstract>We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.
Nous prouvons une identité conjecturée par Adin et Roichman impliquant les ensembles des descentes des permutations cycliques $\lambda$-unimodales. Ces permutations apparaissent dans les formules des caractères pour certaines représentations du groupe symétrique, et ces formules sont généralement prouvées dans une manière algébrique. Ici, nous donnons une preuve combinatoire pour une telle formule et discutons les conséquences pour la distribution de l’ensemble des descentes sur des permutations cycliques.</abstract><pub>DMTCS</pub><doi>10.46298/dmtcs.2411</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1365-8050 |
| ispartof | Discrete mathematics and theoretical computer science, 2014-01, Vol.DMTCS Proceedings vol. AT,... (Proceedings), p.417-428 |
| issn | 1365-8050 1462-7264 1365-8050 |
| language | eng |
| recordid | cdi_doaj_primary_oai_doaj_org_article_f0faef00a8134169952174ee863a5fdb |
| source | Publicly Available Content Database |
| subjects | [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] characters of representations of the symmetric group Combinatorics Computer Science cyclic permutation descent Discrete Mathematics Mathematics necklaces |
| title | Descents of $\lambda$-unimodal cyclic permutations |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T06%3A45%3A30IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_doaj_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Descents%20of%20$%5Clambda$-unimodal%20cyclic%20permutations&rft.jtitle=Discrete%20mathematics%20and%20theoretical%20computer%20science&rft.au=Archer,%20Kassie&rft.date=2014-01-01&rft.volume=DMTCS%20Proceedings%20vol.%20AT,...&rft.issue=Proceedings&rft.spage=417&rft.epage=428&rft.pages=417-428&rft.issn=1365-8050&rft.eissn=1365-8050&rft_id=info:doi/10.46298/dmtcs.2411&rft_dat=%3Chal_doaj_%3Eoai_HAL_hal_01207601v1%3C/hal_doaj_%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c1361-b2bbff643a4d990e0ff5ae26e8e933f54d54215598466ac664cb252f95dc01513%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |