Eulerian polynomials of type $D$ have only real roots
We give an intrinsic proof of a conjecture of Brenti that all the roots of the Eulerian polynomial of type $D$ are real and a proof of a conjecture of Dilks, Petersen, and Stembridge that all the roots of the affine Eulerian polynomial of type $B$ are real, as well.
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2321/pdf |
| _version_ | 1797270310780665856 |
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| author | Carla D. Savage Mirkó Visontai |
| author_facet | Carla D. Savage Mirkó Visontai |
| author_sort | Carla D. Savage |
| collection | DOAJ |
| description | We give an intrinsic proof of a conjecture of Brenti that all the roots of the Eulerian polynomial of type $D$ are real and a proof of a conjecture of Dilks, Petersen, and Stembridge that all the roots of the affine Eulerian polynomial of type $B$ are real, as well. |
| first_indexed | 2024-04-25T02:02:15Z |
| format | Article |
| id | doaj.art-d02a529386d1474a9efc62764230a318 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:15Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-d02a529386d1474a9efc62764230a3182024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.23212321Eulerian polynomials of type $D$ have only real rootsCarla D. Savage0Mirkó Visontai1Department of Mathematics [Raleigh]Department of Mathematics Stockholm UniversityWe give an intrinsic proof of a conjecture of Brenti that all the roots of the Eulerian polynomial of type $D$ are real and a proof of a conjecture of Dilks, Petersen, and Stembridge that all the roots of the affine Eulerian polynomial of type $B$ are real, as well.https://dmtcs.episciences.org/2321/pdfpolynomials with only real roots.inversion sequencescoxeter group of type deulerian polynomials[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Carla D. Savage Mirkó Visontai Eulerian polynomials of type $D$ have only real roots Discrete Mathematics & Theoretical Computer Science polynomials with only real roots. inversion sequences coxeter group of type d eulerian polynomials [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Eulerian polynomials of type $D$ have only real roots |
| title_full | Eulerian polynomials of type $D$ have only real roots |
| title_fullStr | Eulerian polynomials of type $D$ have only real roots |
| title_full_unstemmed | Eulerian polynomials of type $D$ have only real roots |
| title_short | Eulerian polynomials of type $D$ have only real roots |
| title_sort | eulerian polynomials of type d have only real roots |
| topic | polynomials with only real roots. inversion sequences coxeter group of type d eulerian polynomials [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2321/pdf |
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