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Is there a standard name for a partition of a set in which every block (i.e. the subsets comprising the partition) has the same size? Regular? Uniform? Something else? Nothing else (so I'm free to make up my own)?

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This paper uses the term uniform: combinatorics.org/Volume_12/PDF/v12i1r40.pdf. –  Srivatsan Sep 16 '11 at 2:53
I've seen $k$-subset partition being used... –  J. M. Sep 16 '11 at 2:55
Apparently, the term $k$-regular could mean something very different: math.furman.edu/~dpenn/Research/lregularpreprint.pdf and liafa.jussieu.fr/~lovejoy/3regular.pdf. (Note: I have no experience with this field. I just picked the top results from google.) –  Srivatsan Sep 16 '11 at 2:58
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