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Posets :: moebiusFunction(Poset,Thing,Thing)

moebiusFunction(Poset,Thing,Thing) -- returns the Moebius function values for the minimal element of a closed interval to each element of the interval

Synopsis

Description

For elements a and b of a poset P, this routine returns the Mobius function values for the minimal element in the closed interval between elements a and b to each element of the interval between a and b. The routine handles both of the cases a<b and b<a.
i1 : P = poset({a,b,c,d,e,f,g}, {(a,b), (a,c), (a,d), (b,e), (c,e), (c,f), (d,f), (e,g), (f,g)})

o1 = Poset{cache => CacheTable{}                                                                }
           GroundSet => {a, b, c, d, e, f, g}
           RelationMatrix => | 1 1 1 1 1 1 1 |
                             | 0 1 0 0 1 0 1 |
                             | 0 0 1 0 1 1 1 |
                             | 0 0 0 1 0 1 1 |
                             | 0 0 0 0 1 0 1 |
                             | 0 0 0 0 0 1 1 |
                             | 0 0 0 0 0 0 1 |
           Relations => {(a, b), (a, c), (a, d), (b, e), (c, e), (c, f), (d, f), (e, g), (f, g)}

o1 : Poset
i2 : moebiusFunction(P,b,g)

o2 = HashTable{b => 1 }
               e => -1
               g => 0

o2 : HashTable
i3 : moebiusFunction(P,g,b)

o3 = HashTable{b => 1 }
               e => -1
               g => 0

o3 : HashTable

See also