Moussa Benoumhani

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Let L(n, k) = n n−k n−k k. We prove that all the zeros of the polynomial L n (x) = k≥0 L(n, k)x k are real. The sequence L(n, k) is thus strictly log-concave, and hence unimodal with at most two consecutive maxima. We determine those integers where the maximum is reached. In the last section we prove that L(n, k) satisfies a central limit theorem as well as(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 t N 0 (n, k), the number of all unlabeled non-T 0 topologies on E with k open sets, for 3 ≤ k ≤ 8.
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