Combinatorics

Discrete mathematics

Pure mathematics

Mathematics

Programming language

Computer science

Dedekind cut

Continuation

Partition (number theory)

Modular form

Journal of Number Theory

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.

MacMahon's partition analysis XIII: Schmidt type partitions and modular forms