Interlacing of zeroes of certain real-rooted polynomials

Dey, HK (2023) Interlacing of zeroes of certain real-rooted polynomials. In: Archiv der Mathematik .

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Abstract

Combinatorics is full of examples of real-rooted polynomials. Suppose one has a sequence of real-rooted polynomials, and then wants consecutive pairs to have interlacing roots (on the real line). The method of proving the real-rootedness sometimes does not prove the interlacing property. In this work, we prove that if a sequence of real-rooted polynomials satisfies a particular type of recurrence with some conditions, then the sequence also satisfies the interlacing property. We give examples of several interesting combinatorial families of sequences whose interlacingness directly follows from our main result. © 2023, Springer Nature Switzerland AG.

Item Type:	Journal Article
Publication:	Archiv der Mathematik
Publisher:	Birkhauser
Additional Information:	The copyright of this article belongs to Birkhauser.
Keywords:	Eulerian polynomials; Interlacing; Real-rootedness; Stirling permutations
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	12 Mar 2023 05:49
Last Modified:	12 Mar 2023 05:49
URI:	https://eprints.iisc.ac.in/id/eprint/80953

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