K-promotion on m-packed labelings of posets.
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| Title: | K-promotion on m-packed labelings of posets. |
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| Authors: | Kimble, Jamie1, Sagan, Bruce E.1, Dizier, Avery St.1 |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). 2026, Vol. 28 Issue 2, p1-24. 24p. |
| Subjects: | Partially ordered sets, Algebraic combinatorics |
| Abstract: | Schutzenberger’s promotion operator ¨ ∂ is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But ∂ was subsequently shown to have interesting properties when applied to natural labelings of other posets. Pechenik defined a K-theoretic version of promotion, ∂K, on mpacked labelings of tableaux. The operator ∂K was then extended to increasing labelings of other posets. The purpose of the current work is to show that the original action of ∂K on m-packed labelings yields interesting results when applied to partially ordered sets in general, and to rooted trees in particular. We show that under certain conditions, the sizes of the orbits and order of ∂K exhibit nice divisibility properties. We also completely determine, for certain values of m, the orbit sizes for the action on various types of rooted trees such as extended stars, combs, zippers, and a type of three-leaved tree. [ABSTRACT FROM AUTHOR] |
| Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 193021527 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: K-promotion on m-packed labelings of posets. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kimble%2C+Jamie%22">Kimble, Jamie</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Sagan%2C+Bruce+E%2E%22">Sagan, Bruce E.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Dizier%2C+Avery+St%2E%22">Dizier, Avery St.</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Discrete+Mathematics+%26+Theoretical+Computer+Science+%28DMTCS%29%22">Discrete Mathematics & Theoretical Computer Science (DMTCS)</searchLink>. 2026, Vol. 28 Issue 2, p1-24. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Partially+ordered+sets%22">Partially ordered sets</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+combinatorics%22">Algebraic combinatorics</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Schutzenberger’s promotion operator ¨ ∂ is a fundamental map in dynamical algebraic combinatorics. At first, its action was mainly considered on standard Young tableaux. But ∂ was subsequently shown to have interesting properties when applied to natural labelings of other posets. Pechenik defined a K-theoretic version of promotion, ∂K, on mpacked labelings of tableaux. The operator ∂K was then extended to increasing labelings of other posets. The purpose of the current work is to show that the original action of ∂K on m-packed labelings yields interesting results when applied to partially ordered sets in general, and to rooted trees in particular. We show that under certain conditions, the sizes of the orbits and order of ∂K exhibit nice divisibility properties. We also completely determine, for certain values of m, the orbit sizes for the action on various types of rooted trees such as extended stars, combs, zippers, and a type of three-leaved tree. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Discrete Mathematics & Theoretical Computer Science (DMTCS) is the property of Discrete Mathematics & Theoretical Computer Science DMTCS and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 1 Subjects: – SubjectFull: Partially ordered sets Type: general – SubjectFull: Algebraic combinatorics Type: general Titles: – TitleFull: K-promotion on m-packed labelings of posets. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kimble, Jamie – PersonEntity: Name: NameFull: Sagan, Bruce E. – PersonEntity: Name: NameFull: Dizier, Avery St. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13658050 Numbering: – Type: volume Value: 28 – Type: issue Value: 2 Titles: – TitleFull: Discrete Mathematics & Theoretical Computer Science (DMTCS) Type: main |
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