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Undid revision 1170888084 by David Eppstein (talk) The source is mentioned at https://mathematica.stackexchange.com/questions/288395/how-to-make-a-function-that-returns-all-super-distinct-partitions. |
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=== <math display="block">\sum^{MN}_{n=0}p(N,M;n)q^n = {M+N \choose M}_q.</math>Super distinct partitions ===
A super distinct partition if every difference is at least 2. For example, there are seven super distinct partitions of 11: <nowiki>{{11}, {10,1},{9,2},{8,3},{7,4},{7,3,1},{6,4,1}}</nowiki>. The partitions that with distinct parts that are not super distinct are <nowiki>{{8,2,1},{6,5},{6,3,2},{5,4,2},{5,3,2,1}}</nowiki>. The number of partitions of n into super distinct partitions is equivalent to the number of partitions of n into distinct parts such that every even part has a value greater than 2 times the number of odd parts present. This can be written in partition notation as p(n | super-distinct parts) = p(n | distinct parts, every even part > 2 (number of odd parts)). For n=11, we would have <nowiki>{{11},{10,1},{8,3},{7,4},{7,3,1},{6,4,1},{6,5}}</nowiki>.
==Rank and Durfee square==
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