Visontai, Mirkó and Williams, Nathan - 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)
Les polynômes eul\IeC èriens stables de type B

Authors: Visontai, Mirkó and Williams, Nathan

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.


Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
Section: Proceedings
Published on: January 1, 2012
Submitted 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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