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1. Definition & Example

the 7 Cores of size (5, 6)
  ([5],6)   ([4,1],6)   ([3,2],6)   ([3,1,1],6)   ([2,2,1],6)   ([2,1,1,1],6)   ([1,1,1,1,1],6)

2. Properties

3. $(a,b)$-cores

See [AHJ14] for open questions and conjectures concerning $(a,b)$-cores relating to generalized Catalan numbers and $q,t$-Catalan numbers.

4. References

5. Sage examples

6. Technical information for database usage