Geodesic
On the Number of Maximal Elements in a Partially Ordered Set
Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 351-357

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DOI

Let P be a partially ordered set. For an element x ∊ P, a subset C of P is called a cutset for x in P if every element of C is noncomparable to x and every maximal chain in P meets {x} ∪ C. The following result is established: if every element of P has a cutset having n or fewer elements, then P has at most 2n maximal elements. It follows that, if some element of P covers k elements of P then there is an element x ∊ P such that every cutset for x in P has at least log2k elements.
DOI : 10.4153/CMB-1987-050-6
Mots-clés : 06A10, Partially ordered set, cutset, maximal element 
Ginsburg, John. On the Number of Maximal Elements in a Partially Ordered Set. Canadian mathematical bulletin, Tome 30 (1987) no. 3, pp. 351-357. doi: 10.4153/CMB-1987-050-6
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