Geodesic
Les polynômes eul\IeC èriens stables de type B
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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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. 
@article{DMTCS_2012_special_263_a26,
     author = {Visontai, Mirk\'o and Williams, Nathan},
     title = {Les polyn\^omes {eul\IeC} \`eriens stables de type {B}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3040/}
}
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Visontai, Mirkó; Williams, Nathan. Les polynômes eul\IeC èriens stables de type B. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3040. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3040/

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