The Rank and Minimal Border Strip Decompositions of a Skew Partition

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In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: Stanley R.P.

Author: Stanley R.P.

Source: Journal of Combinatorial Theory, Series A, Volume 100, Number 2, November 2002 , pp. 349-375(27)

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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 / and the minimal number of border strips whose union is /. 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. © 2002 Elsevier Science (USA).