On the admissible values of a parameter for maximal Sperner families of subsets of type $(k,k+1)$

In this paper we generalize one assertion (obtained by us earlier) on admissible values of a certain parameter for partial maximal Sperner families (m. s. f.) of subsets of a finite set of the type $(k,k+1)$. We also prove that the minimal value of the parameter under consideration for all m. s. f. of the type $(k,k+1)$, except for two families, is less than $\tbinom{n-1}{k}-1$.