Smith normal form of a multivariate matrix associated with partitions
Author(s)
Bessenrodt, Christine; Stanley, Richard P
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Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant 1 in terms of lattice paths. Here we generalize this result by refining the matrix entries to be multivariate polynomials, and by determining not only the determinant but also the Smith normal form of these matrices. A priori the Smith form need not exist but its existence follows from the explicit computation. It will be more convenient for us to state our results in terms of partitions rather than lattice paths.
Date issued
2014-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Journal of Algebraic Combinatorics
Publisher
Springer US
Citation
Bessenrodt, Christine, and Richard P. Stanley. “Smith Normal Form of a Multivariate Matrix Associated with Partitions.” Journal of Algebraic Combinatorics 41.1 (2015): 73–82.
Version: Author's final manuscript
ISSN
0925-9899
1572-9192