✦ LIBER ✦
The Rank and Minimal Border Strip Decompositions of a Skew Partition
✍ Scribed by Richard P. Stanley
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 257 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
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 l=m and the minimal number of border strips whose union is l=m: 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.