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According to [Dilworth 1950], this cardinality p equals the minimum number of disjoint antichains into which '''M''' can be decomposed. Note that such a decomposition into the minimal number p of disjoint antichains may not be unique.
'''Contours'''
Forward Contours FC[''k''] of ''class k'' are defined inductively, as follows:
FC[0] consists of those elements m1 for which there exists no element m2 such that m2 < m1.
FC[''k''] consists of those elements m1 for which there exists no element m2 such that m2 < m1; and where neither m1 nor m2 are contained in FC[''l''] for any ''class l'' < ''k''.
Reverse Contours RC[''k''] of ''class k'' are defined similarly.
Members of the Meet (∧), or ''Infimum'' of a Forward Contour are referred to as its Dominant Matches: those m1 for which there exists no m2 such that m2 < m1.
Members of the Join (∨), or ''Supremum'' of a Reverse Contour are referred to as its Dominant Matches: those m1 for which there exists no m2 such that m2 > m1.
Where multiple Dominant Matches exist within a Meet (or within a Join, respectively) the Dominant Matches will be incomparable to each other.
'''Background'''
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