TY - JOUR
T1 - On the parity of the number of (a, b, m)-copartitions of n
AU - Burson, Hannah E.
AU - Eichhorn, Dennis
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2023/10/1
Y1 - 2023/10/1
N2 - We continue the study of the (a,b,m)-copartition function cpa,b,m(n), which arose as a combinatorial generalization of Andrews' partitions with even parts below odd parts. The generating function of cpa,b,m(n) has a nice representation as an infinite product. In this paper, we focus on the parity of cpa,b,m(n). We find specific cases of a,b,m such that cpa,b,m(n) is even with density 1. Additionally, we show that the sequence {cpa,m-a,m(n)}n=0∞ takes both even and odd values infinitely often.
AB - We continue the study of the (a,b,m)-copartition function cpa,b,m(n), which arose as a combinatorial generalization of Andrews' partitions with even parts below odd parts. The generating function of cpa,b,m(n) has a nice representation as an infinite product. In this paper, we focus on the parity of cpa,b,m(n). We find specific cases of a,b,m such that cpa,b,m(n) is even with density 1. Additionally, we show that the sequence {cpa,m-a,m(n)}n=0∞ takes both even and odd values infinitely often.
KW - Copartitions
KW - parity
KW - partitions
KW - q -series
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U2 - 10.1142/S1793042123501099
DO - 10.1142/S1793042123501099
M3 - Article
AN - SCOPUS:85165913959
SN - 1793-0421
VL - 19
SP - 2241
EP - 2254
JO - International Journal of Number Theory
JF - International Journal of Number Theory
IS - 9
ER -