A set of linear extensions of is said to " reverse " a critical pair in if there exists a linear extension in for which occurs earlier than.
12.
A set of linear extensions of is said to " reverse " a critical pair in if there exists a linear extension in for which occurs earlier than.
13.
Alternatively, a linear extension may be viewed as an order-preserving bijection from a partially ordered set " P " to a chain " C " on the same ground set.
14.
In turn, Clifford's ideas had emerged from the mid-19th-century work of the German mathematician Hermann Grassmann in his " Lineale Ausdehnungslehre " ( " Theory of Linear Extensions " ).
15.
The Frasier Crane of " Frasier " is not the Frasier Crane of " Cheers " because " Frasier " is not quite a linear extension of " Cheers ."
16.
Due to the linear extension of fibrosis, neither a stenotic area resection nor end-end anastomosis were feasible while the implementation of synthetic material or metallic stent was also not possible.
17.
Among all partial orders with a fixed number of elements and a fixed number of comparable pairs, the partial orders that have the largest number of linear extensions are semiorders.
18.
This property may be used to characterize realizers of finite partial orders : A nonempty set of linear extensions is a realizer if and only if it reverses every critical pair.
19.
They may be the result of a single phase of construction, or be the result of the addition of one or more linear extensions to the bank of a pre-existing barrow.
20.
He was a research student at the University of Cambridge and obtained his PhD in 1988 writing on " Linear Extensions of Partially Ordered Sets " under the supervision of B�la Bollob�s.
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