Combinatorial and Additive Number Theory II by Melvyn B. Nathanson

Author:Melvyn B. Nathanson
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Now it is easy to see that partitions with parts appearing fewer then m times conjugate to partitions with differences less than m and smallest part less than m. For the remainder of this paper, we will call the latter m-flat partitions, after [1].

Remark 1

: A direct map between m-flat and m-regular partitions was developed in [1], translated from the German in an appendix to [2]. (Rather, several involutions on all partitions were constructed, some of which restrict to a map between these sets.) The fixed points are, again, those that simultaneously satisfy both conditions.

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