Authors: Dodig, Marija 
Stošić, Marko 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Combinatorics of polynomial chains
Journal: Linear Algebra and Its Applications
Volume: 589
First page: 130
Last page: 157
Issue Date: 15-Mar-2020
Rank: M21
ISSN: 0024-3795
DOI: 10.1016/j.laa.2019.12.028
Abstract: 
In this paper we consider two polynomial chains and we study the existence of an intermediate polynomial chain satisfying interlacing inequality relations together with some convexity-like properties that arise from applications in completion problems. The presented result is a vast generalisation of existing results dealing with intermediate polynomial chains. The proof of the main result is completely novel to the field, different from all the existing methods used in similar problems. The obtained necessary and sufficient conditions are simple, explicit and constructive.
Keywords: Completion of matrix pencils | Convexity | Polynomial chains
Publisher: Elsevier
Project: Geometry, Education and Visualization With Applications 
Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
FCT, project ISFL-1-1431

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