Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 73-82 |
| Seitenumfang | 10 |
| Fachzeitschrift | Journal of algebraic combinatorics |
| Jahrgang | 41 |
| Ausgabenummer | 1 |
| Frühes Online-Datum | 13 Mai 2014 |
| Publikationsstatus | Veröffentlicht - 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
Zitieren
- Standard
- Harvard
- Apa
- Vancouver
- BibTex
- RIS
in: Journal of algebraic combinatorics, Jahrgang 41, Nr. 1, 02.2015, S. 73-82.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -