The Rank and Minimal Border Strip Decompositions of a Skew Partition

Abstract

The rank of an ordinary partition of a nonnegative integer n is the length of the main diagonal of its Ferrers or Young diagram. Nazarov and Tarasov gave a generalization of this definition for skew partitions and proved some basic properties. We show the close connection between the rank of a skew partition λ/μ and the minimal number of border strips whose union is λ/μ. A general theory of minimal border strip decompositions is developed and an application is given to the evaluation of certain values of irreducible characters of the symmetric group.