Authors: Dodig, Marija 
Stošić, Marko 
Title: On properties of the generalized majorization
Journal: Electronic Journal of Linear Algebra
Volume: 26
First page: 471
Last page: 509
Issue Date: 6-Aug-2013
Rank: M22
ISSN: 1537-9582
URL: https://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol26_pp471-509.pdf
Abstract: 
In this paper, a complete solution of a problem involving generalized majorization of partitions is given: for two pairs of partitions (d, a) and (c, b) necessary and sufficient conditions for the existence of a partition g that is majorized by both pairs is determined. The obtained conditions are explicit, the solution is constructive and it uses novel techniques and indices. Although the problem is motivated by the applications in matrix pencil completions problems, all results are purely combinatorial and they give a new perspective on comparison of partitions.
Keywords: Generalized majorization | Matrix completion | Partitions
Publisher: International Linear Algebra Society
Project: FCT, project ISFL-1-1431
Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Geometry, Education and Visualization With Applications 

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