# flagPoset -- computes the subposet of specified ranks of a ranked poset

## Synopsis

• Usage:
F = flagPoset(P, L)
• Inputs:
• P, an instance of the type Poset,
• L, a list, containing rank indices
• Outputs:
• F, an instance of the type Poset, the subposet of $P$ of only the ranks specified in $L$

## Description

The flag poset with respect to a list of rank indices is the subposet induced by the specified ranks. The maximal chains of the flag poset can be computed with the flagChains method.

 i1 : P = booleanLattice 4; i2 : rankFunction P o2 = {0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4} o2 : List i3 : flagPoset(P, {2,3}) o3 = Relation Matrix: | 1 0 0 1 0 0 1 0 0 0 | | 0 1 0 1 0 0 0 0 1 0 | | 0 0 1 1 0 0 0 0 0 1 | | 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 1 0 1 0 1 0 | | 0 0 0 0 0 1 1 0 0 1 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 1 1 1 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 1 | o3 : Poset i4 : flagPoset(P, {1}) o4 = Relation Matrix: | 1 0 0 0 | | 0 1 0 0 | | 0 0 1 0 | | 0 0 0 1 | o4 : Poset

## See also

• flagChains -- computes the maximal chains in a list of flags of a ranked poset
• isRanked -- determines if a poset is ranked
• rankPoset -- generates a list of lists representing the ranks of a ranked poset

## Ways to use flagPoset :

• "flagPoset(Poset,List)"

## For the programmer

The object flagPoset is .