TY - JOUR
T1 - Marking and Shifting a Part in Partitions
AU - O’Hara, Kathleen
AU - Stanton, Dennis
PY - 2019/11/1
Y1 - 2019/11/1
N2 - Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers–Ramanujan identities, the Göllnitz–Gordon identities, Euler’s odd = distinct theorem, and the Andrews–Gordon identities. Generalizations of each of these theorems are given where a single part is “marked” or weighted. This allows a single part to be replaced by a new larger part, “shifting” a part, and analogous combinatorial results are given in each case. Versions are also given for marking a sum of parts.
AB - Refined versions, analytic and combinatorial, are given for classical integer partition theorems. The examples include the Rogers–Ramanujan identities, the Göllnitz–Gordon identities, Euler’s odd = distinct theorem, and the Andrews–Gordon identities. Generalizations of each of these theorems are given where a single part is “marked” or weighted. This allows a single part to be replaced by a new larger part, “shifting” a part, and analogous combinatorial results are given in each case. Versions are also given for marking a sum of parts.
KW - Partition
KW - Rogers–Ramanujan identities
UR - http://www.scopus.com/inward/record.url?scp=85074557662&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85074557662&partnerID=8YFLogxK
U2 - 10.1007/s00026-019-00448-5
DO - 10.1007/s00026-019-00448-5
M3 - Article
AN - SCOPUS:85074557662
SN - 0218-0006
VL - 23
SP - 935
EP - 951
JO - Annals of Combinatorics
JF - Annals of Combinatorics
IS - 3-4
ER -