Change search
ReferencesLink to record
Permanent link

Direct link
Stable multivariate W-Eulerian polynomials
University of Pennsylvania, United States.
2013 (English)In: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 120, no 7, 1929-1945 p.Article in journal (Refereed) Published
Abstract [en]

We prove a multivariate strengthening of Brenti's result that every root of the Eulerian polynomial of type B 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. Our results extend naturally to colored permutations, and we also give stable generalizations of recent real-rootedness results due to Dilks, Petersen, and Stembridge on affine Eulerian polynomials of types A and C. Finally, although we are not able to settle Brenti's real-rootedness conjecture for Eulerian polynomials of type D. nor prove a companion conjecture of Dilks, Petersen, and Stembridge for affine Eulerian polynomials of types B and D. we indicate some methods of attack and pose some related open problems.

Place, publisher, year, edition, pages
2013. Vol. 120, no 7, 1929-1945 p.
Keyword [en]
Eulerian polynomials, Descent set, Coxeter groups, Differential recurrence, Real roots only, Real stability, Catalan numbers
National Category
URN: urn:nbn:se:kth:diva-129447DOI: 10.1016/j.jcta.2013.07.009ISI: 000323868200037OAI: diva2:652864

QC 20131002

Available from: 2013-10-02 Created: 2013-09-30 Last updated: 2013-10-02Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Visontai, Mirko
In the same journal
Journal of combinatorial theory. Series A (Print)

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 13 hits
ReferencesLink to record
Permanent link

Direct link