MacMahon's partition analysis XIII: Schmidt type partitions and modular forms
The study of MacMahon's partition analysis has been the topic of twelve papers written by these two prolific authors. This article has been inspired by a problem of Frank Schmidt related to interrupted partitions. The authors provide a context for this result which leads directly to many other theorems of this nature. Thus, a number of Schmidt type partitions arising from partitions on various graphs will be seen to have modular forms as generating functions. Some conjectures concerning congruences living on arithmetic subsequences of Schmidt type partition numbers are stated. This paper spurs the interest to find further natural arithmetic/combinatorial objects generated by modular forms.
scientific article; zbMATH DE number 7466544
scientific article