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Posets :: moebiusFunction

moebiusFunction -- computes the Moebius function at every pair of elements of a poset

Synopsis

Description

The Moebius function of P is a function defined at pairs of vertices of P with the properties: mu(a,a) = 1 for all a in P, and mu(a,b) = -sum(mu(a,c)) over all a ≤c < b.

The Moebius function of the n chain is 1 at (a,a) for all a, -1 at (a, a+1) for 1 ≤a < n, and 0 every where else.
i1 : moebiusFunction chain 3

o1 = HashTable{(1, 1) => 1 }
               (1, 2) => -1
               (1, 3) => 0
               (2, 1) => 0
               (2, 2) => 1
               (2, 3) => -1
               (3, 1) => 0
               (3, 2) => 0
               (3, 3) => 1

o1 : HashTable

Ways to use moebiusFunction :