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. 
@article{IVM_2008_6_a2,
     author = {B. S. Kochkarev},
     title = {On the admissible values of a parameter for maximal {Sperner} families of subsets of type $(k,k+1)$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--28},
     publisher = {mathdoc},
     number = {6},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_6_a2/}
}
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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/