Abstract
Successive ranks of a partition, which were introduced by Atkin, are the difference of the lengths of the i-th row and the i-th column in the Ferrers graph. Recently, in the study of singular overpartitions, Andrews revisited successive ranks and parity blocks. Motivated by his work, we investigate partitions with prescribed successive rank parity blocks. The main result of this paper is the generating function of partitions with exactly d successive ranks and m parity blocks.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 12-35 |
| Number of pages | 24 |
| Journal | Journal of Combinatorial Theory. Series A |
| Volume | 158 |
| DOIs | |
| State | Published - Aug 1 2018 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
Cite this
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Enumeration of partitions with prescribed successive rank parity blocks. / Seo, Seunghyun; Yee, Ae Ja.
In: Journal of Combinatorial Theory. Series A, Vol. 158, 01.08.2018, p. 12-35.Research output: Contribution to journal › Article
TY - JOUR
T1 - Enumeration of partitions with prescribed successive rank parity blocks
AU - Seo, Seunghyun
AU - Yee, Ae Ja
PY - 2018/8/1
Y1 - 2018/8/1
N2 - Successive ranks of a partition, which were introduced by Atkin, are the difference of the lengths of the i-th row and the i-th column in the Ferrers graph. Recently, in the study of singular overpartitions, Andrews revisited successive ranks and parity blocks. Motivated by his work, we investigate partitions with prescribed successive rank parity blocks. The main result of this paper is the generating function of partitions with exactly d successive ranks and m parity blocks.
AB - Successive ranks of a partition, which were introduced by Atkin, are the difference of the lengths of the i-th row and the i-th column in the Ferrers graph. Recently, in the study of singular overpartitions, Andrews revisited successive ranks and parity blocks. Motivated by his work, we investigate partitions with prescribed successive rank parity blocks. The main result of this paper is the generating function of partitions with exactly d successive ranks and m parity blocks.
UR - http://www.scopus.com/inward/record.url?scp=85044142201&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85044142201&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2018.03.004
DO - 10.1016/j.jcta.2018.03.004
M3 - Article
AN - SCOPUS:85044142201
VL - 158
SP - 12
EP - 35
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
SN - 0097-3165
ER -