A grammar of Dumont and a theorem of Diaconis-Evans-Graham.
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| Title: | A grammar of Dumont and a theorem of Diaconis-Evans-Graham. |
|---|---|
| Authors: | Chen, William Y.C.1 (AUTHOR) chenyc@tju.edu.cn, Fu, Amy M.1,2 (AUTHOR) fu.mei@mail.shufe.edu.cn |
| Source: | Advances in Applied Mathematics. Sep2024, Vol. 160, pN.PAG-N.PAG. 1p. |
| Subjects: | Generating functions, Inheritance & succession, Point set theory, Bijections, Grammar |
| Abstract: | We came across an unexpected connection between a remarkable grammar of Dumont for the joint distribution of (exc , fix) over S n and a beautiful theorem of Diaconis-Evans-Graham on successions and fixed points of permutations. With the grammar in hand, we demonstrate the advantage of the grammatical calculus in deriving the generating functions, where the constant property plays a substantial role. On the grounds of left successions of a permutation, we present a grammatical treatment of the joint distribution investigated by Roselle. Moreover, we obtain a left succession analogue of the Diaconis-Evans-Graham theorem, exemplifying the idea of a grammar assisted bijection. The grammatical labelings give rise to an equidistribution of (jump , des) and (exc , drop) restricted to the set of left successions and the set of fixed points, where jump is defined to be the number of ascents minus the number of left successions. [ABSTRACT FROM AUTHOR] |
| Copyright of Advances in Applied Mathematics is the property of Academic Press Inc. 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 179368630 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.aam.2024.102743 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 1 StartPage: N.PAG Subjects: – SubjectFull: Generating functions Type: general – SubjectFull: Inheritance & succession Type: general – SubjectFull: Point set theory Type: general – SubjectFull: Bijections Type: general – SubjectFull: Grammar Type: general Titles: – TitleFull: A grammar of Dumont and a theorem of Diaconis-Evans-Graham. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chen, William Y.C. – PersonEntity: Name: NameFull: Fu, Amy M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 01968858 Numbering: – Type: volume Value: 160 Titles: – TitleFull: Advances in Applied Mathematics Type: main |
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