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# flagChains -- computes the maximal chains in a list of flags of a ranked poset

- Usage:
    `C = flagChains(P, L)`
- Inputs:
  - P, an instance of the type Poset,
  - L, a list, containing rank indices
- Outputs:
  - C, a list, all maximal chains of $P$ containing only elements in the flags indexed by $L$

## Description

The flag chains of $P$ with respect to $L$ are exactly the maximalChains of the flagPoset of $P$ with respect to $L$.

    i1 : D = divisorPoset(2^2*3*5);

    i2 : rankFunction D

    o2 = {0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4}

    o2 : List

    i3 : flagChains(D, {1,2,3})

    o3 = {{2, 4, 12}, {2, 6, 12}, {3, 6, 12}, {2, 4, 20}, {2, 10, 20}, {5, 10,
         ------------------------------------------------------------------------
         20}, {2, 6, 30}, {3, 6, 30}, {2, 10, 30}, {5, 10, 30}, {3, 15, 30}, {5,
         ------------------------------------------------------------------------
         15, 30}}

    o3 : List

## See also

- flagPoset -- computes the subposet of specified ranks of a ranked poset
- isRanked -- determines if a poset is ranked
- maximalChains -- computes all maximal chains of a poset
- rankPoset -- generates a list of lists representing the ranks of a ranked poset

## Ways to use flagChains:

- `flagChains(Poset,List)`

## For the programmer

The object flagChains is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Posets.m2:4781:0.