Stanley’s zrank conjecture on skew partitions
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- by William Y. C. Chen and Arthur L. B. Yang PDF
- Trans. Amer. Math. Soc. 360 (2008), 3121-3131 Request permission
Abstract:
We present an affirmative answer to Stanley’s zrank conjecture, namely, the zrank and the rank are equal for any skew partition. We show that certain classes of restricted Cauchy matrices are nonsingular and furthermore, the signs are determined by the number of zero entries. We also give a characterization of the rank in terms of the Giambelli-type matrices of the corresponding skew Schur functions. Our approach also applies to the factorial Cauchy matrices and the inverse binomial coefficient matrices.References
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Additional Information
- William Y. C. Chen
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- MR Author ID: 232802
- Email: chen@nankai.edu.cn
- Arthur L. B. Yang
- Affiliation: Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin 300071, People’s Republic of China
- MR Author ID: 744941
- Email: yang@nankai.edu.cn
- Received by editor(s): September 11, 2005
- Received by editor(s) in revised form: April 12, 2006
- Published electronically: January 25, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 3121-3131
- MSC (2000): Primary 05E10, 15A15
- DOI: https://doi.org/10.1090/S0002-9947-08-04342-0
- MathSciNet review: 2379790