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A transitive antisymmetric relation among the elements of a set, which does not necessarily apply to each pair of elements.
‘In terms of sets, a partial ordering can be obtained by using set inclusion, the relation ‘is a subset of,’ where subset also includes the meaning that a set is a subset of itself.’
‘Shoham's theory is based on a partial order over models: S can then be characterized as the set of models in K that are minimal in K.’
‘Viewed another way, what this says is that if we define a partial ordering on strings such that one string is greater than another if it contains the second as a substring, then there is no infinite antichain.’
‘In fact, it can be shown that the possible ancestral combinations of adjacent copies are given by the maximal antichains of the partial order on the duplication events.’
‘An attempt to articulate a range of scenarios in which partial ordering of secondary and tertiary structures mutually enhance a favorable folding pathway has been presented under the label of ‘nucleation-condensation’.’