Key points are not available for this paper at this time.
A collection of families (F₁, F₂, , F₊) P (n) ᵏ is cross-Sperner if there is no pair i = j for which some Fᵢ Fᵢ is comparable to some Fⱼ Fⱼ. Two natural measures of the 'size' of such a family are the sum ₈ = ₁ᵏ |Fᵢ| and the product ₈ = ₁ᵏ |Fᵢ|. We prove new upper and lower bounds on both of these measures for general n and k 2 which improve considerably on the previous best bounds. In particular, we construct a rich family of counterexamples to a conjecture of Gerbner, Lemons, Palmer, Patkós, and Szécsi from 2011.
Behague et al. (Fri,) studied this question.
Synapse has enriched 4 closely related papers on similar clinical questions. Consider them for comparative context: