K-regular Antichains on [m] with K ≤ M-2

نویسنده

  • Matthias Böhm
چکیده

Let 2 be ordered by set inclusion and let B ⊆ 2 be an antichain of size n := |B|. An antichain B is k-regular for some non-negative integer k, if for each i ∈ [m] there are exactly k sets B1, B2, . . . , Bk ∈ B containing i. In this case we say that B is a (k, m, n)-antichain. Let 2 ≤ k ≤ m − 2 be positive integers. In this paper we show that a (k, m, n)-antichain exists if and only if k + 1 ≤ n ≤ km 2 .

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عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 53  شماره 

صفحات  -

تاریخ انتشار 2012