infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic f defined by Frankiewicz. Vojt́ ǎs showedb ≤ f, and Blass showedf ≤ min(d, unif(K )). We show that all the versions coincide and that f is greater than or equal to the splitting number. We prove the consistency of max( b, s) < f and of f < min(d, unif(K )). 

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