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dilworthNumber -- computes the Dilworth number of a poset

Synopsis

Usage:

d = dilworthNumber P
Inputs:
- P, an instance of the type Poset,
Outputs:
- d, an integer, the maximum length of an antichain

Description

The Dilworth number of a poset is the maximum length of an antichain.

The Dilworth number of a chain is always 1.

i1 : n = 5;

i2 : dilworthNumber chain n

o2 = 1

The Dilworth number of the $n$ booleanLattice is $n*(n-1)/2$.

i3 : dilworthNumber booleanLattice n

o3 = 10

i4 : n*(n-1)//2

o4 = 10

See also

antichains -- computes all antichains of a poset
dilworthLattice -- computes the Dilworth lattice of a poset
maximalAntichains -- computes all maximal antichains of a poset

Ways to use dilworthNumber :

dilworthNumber(Poset)

For the programmer

The object dilworthNumber is a method function.