The rank and minimal border strip decompositions of a skew partition

  • Authors:

  • Richard P. Stanley

  • Affiliations:

  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2002

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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.