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Possible database queries for set partitions: search your data / browse all statistics / browse all maps

1. Definition & Example

$$S = P_1 \sqcup P_2 \sqcup \dots \sqcup P_k, \quad P_i \cap P_j = \emptyset \text{ for all }i \neq j, \quad \emptyset \notin \mathcal{P}.$$

The five set partitions of $\{1,2,3\}$

http://www.findstat.org/Graphics/api/Cc0009_0_{{1,2,3} }.png

http://www.findstat.org/Graphics/api/Cc0009_0_{{1},{2,3} }.png

http://www.findstat.org/Graphics/api/Cc0009_0_{{1,3},{2} }.png

http://www.findstat.org/Graphics/api/Cc0009_0_{{1,2},{3} }.png

http://www.findstat.org/Graphics/api/Cc0009_0_{{1},{2},{3} }.png

 {{1,2,3}} 

 {{1},{2,3}} 

 {{1,3},{2}} 

 {{1,2},{3}} 

 {{1},{2},{3}} 

2. FindStat representation and coverage

3. Additional information

4. References

5. Sage examples


CategoryCombinatorialCollection