Geodesic
On the admissible values of a parameter for maximal Sperner families of subsets of type $(k,k+1)$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 25-28.

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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 $\tbinom{n-1}{k}-1$.
Keywords: a Sperner family. 
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B. S. Kochkarev. On the admissible values of a parameter for maximal Sperner families of subsets of type $(k,k+1)$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2008), pp. 25-28. http://geodesic.mathdoc.fr/item/IVM_2008_6_a2/

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[4] Kochkarev B. S., “Ob odnom klasse maksimalnykh shpernerovykh semeistv podmnozhestv konechnogo mnozhestva”, Problemy sovremennoi matematiki, Materialy nauchnoi konf., posv. 125-letiyu KGPU (Kazan, 22–24 oktyabrya 2001 g.), Tr. matem. tsentra im. N. I. Lobachevskogo, 11, Unipress, Kazan, 2001, 160–162 | MR