The Smith normal form of a matrix associated with Young’s lattice
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- by Tommy Wuxing Cai and Richard P. Stanley PDF
- Proc. Amer. Math. Soc. 143 (2015), 4695-4703 Request permission
Abstract:
We prove a conjecture of Miller and Reiner on the Smith normal form of the operator $DU$ associated with a differential poset for the special case of Young’s lattice. Equivalently, this operator can be described as $\frac {\partial }{\partial p_1}p_1$ acting on homogeneous symmetric functions of degree $n$.References
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Additional Information
- Tommy Wuxing Cai
- Affiliation: School of Sciences, South China University of Technology, Guangzhou 510640, People’s Republic of China
- Email: caiwx@scut.edu.cn
- Richard P. Stanley
- Affiliation: Department of mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 166285
- Email: rstan@math.mit.edu
- Received by editor(s): June 9, 2014
- Received by editor(s) in revised form: August 17, 2014
- Published electronically: June 18, 2015
- Additional Notes: The first author thanks M.I.T. for providing a great research environment, the China Scholarship Council for partial support, and the Combinatorics Center at Nankai University for their hospitality when this work was initiated. The second author was partially supported by NSF grant DMS-1068625.
- Communicated by: Patricia L. Hersh
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4695-4703
- MSC (2000): Primary 05E05; Secondary 17B69, 05E10
- DOI: https://doi.org/10.1090/proc/12642
- MathSciNet review: 3391028