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The Smith normal form of a matrix associated with Young's lattice


Authors: Tommy Wuxing Cai and Richard P. Stanley
Journal: Proc. Amer. Math. Soc. 143 (2015), 4695-4703
MSC (2000): Primary 05E05; Secondary 17B69, 05E10
DOI: https://doi.org/10.1090/proc/12642
Published electronically: June 18, 2015
MathSciNet review: 3391028
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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$.


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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
Email: rstan@math.mit.edu

DOI: https://doi.org/10.1090/proc/12642
Keywords: Young's lattice, Schur function, Smith normal form
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
Article copyright: © Copyright 2015 American Mathematical Society