Smith normal form of a multivariate matrix associated with partitions
Name
10801_2014_Article_527.pdf
Size
181.37 KB
Format
Adobe PDF
Checksum (MD5)
fe5dfac955866d1fc7c19a65d53660d9
Author(s)
Bessenrodt, Christine
Stanley, Richard P
Date Issued
May 2014
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10801-014-0527-4
