2001/09/14 by Richard P. Stanley, Stanley, Richard P.
Mathematics · #05E10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05E10
paper · pdf · doi:10.48550/arxiv.math/0109092
31 pages, 10 figures
arxiv created 2001/09/14 · openalex publication_date 2001/09/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Nazarov and Tarasov recently generalized the notion of the rank of a partition to skew partitions. We give several characterizations of the rank of a skew partition and one possible characterization that remains open. One of the characterizations involves the decomposition of a skew shape into a minimal number of border strips, and we develop a theory of these MBSD's as well as of the closely related minimal border strip tableaux. An application is given to the value of a character of the symmetric group Sn indexed by a skew shape z at a permutation whose number of cycles is the rank of z.