Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9498148 | Linear Algebra and its Applications | 2005 | 15 Pages |
Abstract
The rank of a skew partition λ/μ, denoted rank(λ/μ), is the smallest number r such that λ/μ is a disjoint union of r border strips. Let sλ/μ(1t) denote the skew Schur function sλ/μ evaluated at x1 = â¯Â = xt = 1, xi = 0 for i > t. The zrank of λ/μ, denoted zrank(λ/μ), is the exponent of the largest power of t dividing sλ/μ(1t). Stanley conjectured that rank(λ/μ) = zrank(λ/μ). We show the equivalence between the validity of the zrank conjecture and the nonsingularity of restricted Cauchy matrices. In support of Stanley's conjecture we give affirmative answers for some special cases.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Guo-Guang Yan, Arthur L.B. Yang, Joan J. Zhou,