Two-Part and k-Sperner Families: New Proofs Using Permutations

  • Authors:
  • Péter L. Erdos;Zoltán Füredi;Gyula O. H. Katona

  • Affiliations:
  • -;-;-

  • Venue:
  • SIAM Journal on Discrete Mathematics
  • Year:
  • 2005

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Abstract

This is a paper about the beauty of the permutation method. New and shorter proofs are given for the theorem [P. L. Erdos and G. O. H. Katona, J. Combin. Theory. Ser. A, 43 (1986), pp. 58--69; S. Shahriari, Discrete Math., 162 (1996), pp. 229--238] determining all extremal two-part Sperner families and for the uniqueness of k-Sperner families of maximum size [P. Erdos, Bull. Amer. Math. Soc., 51 (1945), pp. 898--902].