Combinatorics of polynomial chains

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.