i need some clarification about linear ordering: Let R a partial ordering relation : R=( { (1,2),(1,4),(2,7)(3,4),(3,5),(4,6)(5,6)(6,8),(7,8)}, =< )
How many linear extension has R ?
I went to the definition of a linear extension: i saw that a linear extension of a partial ordered set is an extension which is a linear order, so here is what i found :
R* =({(1,2),(1,3)(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8) } =<)
So we have 20 linear extension of R ? is it how we find linear extension of a relation?
Is there a general formula ?
Thanks for help