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Discrete Mathematics & Theoretical Computer Science |
Mirkó Visontai ; Nathan Williams - Les polynômes eul\IeC èriens stables de type B
dmtcs:3040 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3040Les polynômes eul\IeC èriens stables de type BArticle
Authors: Mirkó Visontai 1; Nathan Williams 
2
- 1 Department of Mathematics [Philadelphia]
- 2 School of Mathematics
We give a multivariate analog of the type B Eulerian polynomial introduced by Brenti. We prove that this multivariate polynomial is stable generalizing Brenti's result that every root of the type B Eulerian polynomial is real. Our proof combines a refinement of the descent statistic for signed permutations with the notion of real stability—a generalization of real-rootedness to polynomials in multiple variables. The key is that our refined multivariate Eulerian polynomials satisfy a recurrence given by a stability-preserving linear operator.
Source: HAL:hal-01283169v1
Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Imported on: January 31, 2017
Keywords: type B Eulerian polynomials, polynomials with real roots only, stability,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
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