Limit theorems for fixed point biased permutations avoiding a pattern of length three.
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| Title: | Limit theorems for fixed point biased permutations avoiding a pattern of length three. |
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| Authors: | Chelikavada, Aksheytha1, Panzo, Hugo2 |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). 2026, Vol. 28 Issue 2, p1-17. 17p. |
| Subjects: | Permutations, Limit theorems, Distribution (Probability theory), Phase transitions, Rayleigh model, Gaussian distribution, Negative binomial distribution |
| Abstract: | We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution towards favoring permutations with more or fewer fixed points than is typical under the uniform distribution. One case we study features a phase transition where the limiting distribution changes abruptly from negative binomial to Rayleigh to normal depending on the bias parameter. [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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| Items | – Name: Title Label: Title Group: Ti Data: Limit theorems for fixed point biased permutations avoiding a pattern of length three. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chelikavada%2C+Aksheytha%22">Chelikavada, Aksheytha</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Panzo%2C+Hugo%22">Panzo, Hugo</searchLink><relatesTo>2</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, p1-17. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Permutations%22">Permutations</searchLink><br /><searchLink fieldCode="DE" term="%22Limit+theorems%22">Limit theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Phase+transitions%22">Phase transitions</searchLink><br /><searchLink fieldCode="DE" term="%22Rayleigh+model%22">Rayleigh model</searchLink><br /><searchLink fieldCode="DE" term="%22Gaussian+distribution%22">Gaussian distribution</searchLink><br /><searchLink fieldCode="DE" term="%22Negative+binomial+distribution%22">Negative binomial distribution</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution towards favoring permutations with more or fewer fixed points than is typical under the uniform distribution. One case we study features a phase transition where the limiting distribution changes abruptly from negative binomial to Rayleigh to normal depending on the bias parameter. [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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193021515 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 1 Subjects: – SubjectFull: Permutations Type: general – SubjectFull: Limit theorems Type: general – SubjectFull: Distribution (Probability theory) Type: general – SubjectFull: Phase transitions Type: general – SubjectFull: Rayleigh model Type: general – SubjectFull: Gaussian distribution Type: general – SubjectFull: Negative binomial distribution Type: general Titles: – TitleFull: Limit theorems for fixed point biased permutations avoiding a pattern of length three. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chelikavada, Aksheytha – PersonEntity: Name: NameFull: Panzo, Hugo 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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