Details
| Original language | English |
|---|---|
| Pages (from-to) | 73-82 |
| Number of pages | 10 |
| Journal | Journal of algebraic combinatorics |
| Volume | 41 |
| Issue number | 1 |
| Early online date | 13 May 2014 |
| Publication status | Published - Feb 2015 |
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.
Keywords
- Determinants, Lattice paths, Partitions, q-Catalan number, Smith normal form
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Discrete Mathematics and Combinatorics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of algebraic combinatorics, Vol. 41, No. 1, 02.2015, p. 73-82.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Smith normal form of a multivariate matrix associated with partitions
AU - Bessenrodt, Christine
AU - Stanley, Richard P.
PY - 2015/2
Y1 - 2015/2
N2 - 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.
AB - 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.
KW - Determinants
KW - Lattice paths
KW - Partitions
KW - q-Catalan number
KW - Smith normal form
UR - http://www.scopus.com/inward/record.url?scp=84920549740&partnerID=8YFLogxK
U2 - 10.1007/s10801-014-0527-4
DO - 10.1007/s10801-014-0527-4
M3 - Article
AN - SCOPUS:84920549740
VL - 41
SP - 73
EP - 82
JO - Journal of algebraic combinatorics
JF - Journal of algebraic combinatorics
SN - 0925-9899
IS - 1
ER -