Is there a symbol for set all partitions of a set (like P for Power set)?
P.S. I need such symbol in writing some mathematical related notes.
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2You can use any symbol to represent that, as long as you define it so people know what it means. I'm not sure if there is a commonly used one. – arbitrary username Nov 26 '15 at 19:55
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Did you ever settle on a good notation for this? – Daniel Martin Jul 15 '18 at 01:21
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See this answer to a similar question on MO. I suggest stealing notation from combinatorics and letting $\mathrm{B}_S$ denote the set of partitions of $S$, since the Bell number $\mathrm{B}_{|S|}$ is the number of partitions of $S$.
user76284
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This is the commonly used symbol for the set of all subset of the set $E\:$ : $\mathscr{P}(E)$.
hachemy
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1Thanks hachem, but I need the symbol for the set all partitions of a set. – Tail of Godzilla Nov 26 '15 at 20:04
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wiki definition of partition of a set: "a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets." The set of all partition is a set which contain all partition of a set, e.g., for set A={1,2,3}, the set of all partitions would be B={ { {1}, {2}, {3} }, { {1, 2}, {3} }, { {1, 3}, {2} }, { {1}, {2, 3} }, { {1, 2, 3} }}. – Tail of Godzilla Nov 27 '15 at 04:45