TY - JOUR
T1 - MacMahon's partition analysis XIII
T2 - Schmidt type partitions and modular forms
AU - Andrews, George E.
AU - Paule, Peter
N1 - Funding Information:
The first author was partially supported by Simons Foundation Grant 633 284.The second author was partially supported by SFB Grant F50-06 of the Austrian Science Fund FWF.
Publisher Copyright:
© 2021 The Author(s)
PY - 2022/5
Y1 - 2022/5
N2 - In 1999, Frank Schmidt noted that the number of partitions of integers with distinct parts in which the first, third, fifth, etc., summands add to n is equal to p(n), the number of partitions of n. The object of this paper is to provide a context for this result which leads directly to many other theorems of this nature and which can be viewed as a continuation of our work on elongated partition diamonds. Again generating functions are infinite products built by the Dedekind eta function which, in turn, lead to interesting arithmetic theorems and conjectures for the related partition functions.
AB - In 1999, Frank Schmidt noted that the number of partitions of integers with distinct parts in which the first, third, fifth, etc., summands add to n is equal to p(n), the number of partitions of n. The object of this paper is to provide a context for this result which leads directly to many other theorems of this nature and which can be viewed as a continuation of our work on elongated partition diamonds. Again generating functions are infinite products built by the Dedekind eta function which, in turn, lead to interesting arithmetic theorems and conjectures for the related partition functions.
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U2 - 10.1016/j.jnt.2021.09.008
DO - 10.1016/j.jnt.2021.09.008
M3 - Article
AN - SCOPUS:85119645603
SN - 0022-314X
VL - 234
SP - 95
EP - 119
JO - Journal of Number Theory
JF - Journal of Number Theory
ER -