TY - JOUR
T1 - Enumeration of partitions with prescribed successive rank parity blocks
AU - Seo, Seunghyun
AU - Yee, Ae Ja
N1 - Funding Information:
The second author was partially supported by a grant (#280903) from the Simons Foundation.
Publisher Copyright:
© 2018 Elsevier Inc.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/8
Y1 - 2018/8
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.
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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 -