Moussa Benoumhani

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A positive real sequence (ak) n k=0 is said to be unimodal if there exist integers k0, k1, 0 ≤ k0 ≤ k1 ≤ n such that a0 ≤ a1 ≤ · · · ≤ ak0 = ak0+1 = · · · = ak1 ≥ ak1+1 ≥ · · · ≥ an. The integers l, k0 ≤ l ≤ k1 are called the modes of the sequence. If k0 < k1 then (ak)k=0 is said to have a plateau of k1 − k0 + 1 elements; if k0 = k1 then it is said to have(More)
Let E be a set with n elements, and let T (n, k) be the number of all labeled topologies having k open sets that can be defined on E. In this paper, we compute these numbers for k ≤ 17, and arbitrary n, as well as tN0(n, k), the number of all unlabeled non-T0 topologies on E with k open sets, for 3 ≤ k ≤ 8.
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