On the Number of Maximal Elements in a Partially Ordered Set
1987 ◽
Vol 30
(3)
◽
pp. 351-357
◽
Keyword(s):
AbstractLet 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.
1991 ◽
Vol 34
(1)
◽
pp. 23-30
◽
Keyword(s):
1987 ◽
Vol 30
(4)
◽
pp. 421-428
◽
1969 ◽
Vol 9
(3-4)
◽
pp. 361-362
Keyword(s):
2020 ◽
Vol 9
(10)
◽
pp. 8771-8777
1974 ◽
Vol 17
(4)
◽
pp. 406-413
◽
Keyword(s):
1972 ◽
Vol 13
(4)
◽
pp. 451-455
◽
Keyword(s):
1994 ◽
Vol 03
(02)
◽
pp. 223-231
Keyword(s):