<div class="csl-bib-body">
<div class="csl-entry">Pappe Joseph, Pfannerer-Mittas, S. H., Schilling, A., & Simone, M. C. (2023). Promotion for fans of Dyck paths. In <i>Proceedings of the 35th Conference on Formal Power Series and Algebraic Combinatorics</i>. 35th Conference on Formal Power Series and Algebraic Combinatorics (FPSAC’23), Davis, United States of America (the). http://hdl.handle.net/20.500.12708/192757</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/192757
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dc.description.abstract
We construct an injection from the set of r-fans of Dyck paths of length n into the set of chord diagrams on [n] that intertwines promotion and rotation. This is done in two different ways, namely as fillings of promotion matrices and in terms of Fomin growth diagrams. Our analysis uses the fact that r-fans of Dyck paths can be viewed as highest weight elements of weight zero in crystals of type Br, which in turn can be analyzed using virtual crystals. On the level of Fomin growth diagrams, the virtualization process corresponds to the Roby–Krattenthaler blow up construction. Our construction generalizes to vacillating tableaux as well. We give a cyclic sieving phenomenon on r-fans of Dyck paths using the promotion action.
en
dc.description.sponsorship
Österr. Akademie der Wissenschaften
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dc.language.iso
en
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dc.relation.ispartofseries
Séminaire Lotharingien de Combinatoire
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dc.subject
crystal bases
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dc.subject
promotion
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dc.subject
Fomin growth and chord diagrams
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dc.subject
Dyck paths
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dc.title
Promotion for fans of Dyck paths
en
dc.type
Inproceedings
en
dc.type
Konferenzbeitrag
de
dc.contributor.affiliation
University of California, Davis, United States of America (the)
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dc.contributor.affiliation
University of California, Davis, United States of America (the)
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dc.contributor.affiliation
University of California, Davis, United States of America (the)
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dc.relation.grantno
25658
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dc.type.category
Full-Paper Contribution
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tuw.booktitle
Proceedings of the 35th Conference on Formal Power Series and Algebraic Combinatorics
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tuw.container.volume
89B
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tuw.book.chapter
20
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tuw.publication.invited
invited
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tuw.project.title
Rotationsinvariante diagrammatische Basen für Invariantenräume
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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dc.description.numberOfPages
12
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tuw.event.name
35th Conference on Formal Power Series and Algebraic Combinatorics (FPSAC'23)
en
tuw.event.startdate
17-07-2023
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tuw.event.enddate
21-07-2023
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Davis
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tuw.event.country
US
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tuw.event.institution
UC Davis
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tuw.event.presenter
Pfannerer-Mittas, Stephan Heinz
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.languageiso639-1
en
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item.openairetype
conference paper
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item.grantfulltext
restricted
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item.fulltext
no Fulltext
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item.cerifentitytype
Publications
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item.openairecristype
http://purl.org/coar/resource_type/c_5794
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crisitem.author.dept
University of California, Davis
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crisitem.author.dept
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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crisitem.author.dept
University of California, Davis
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crisitem.author.dept
University of California, Davis
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
