# connectedComponents(Poset) -- generates a list of connected components of a poset

## Synopsis

• Function: connectedComponents
• Usage:
C = connectedComponents P
• Inputs:
• P, an instance of the type Poset,
• Outputs:
• C, a list, containing lists of vertices, each of which is a connected component of $P$

## Description

A connected component of $P$ is a set of vertices of $P$ such that every between every pair of vertices $u$ and $v$ in the set there exists a chain of vertices $(a_0=u,a_1,\ldots,a_n=v)$ such that $a_{i-1}$ and $a_i$ are comparable in $P$ for each $i$.

 i1 : C = chain 3; i2 : connectedComponents C o2 = {{1, 2, 3}} o2 : List i3 : S = sum(5, i -> naturalLabeling(C, 10*i)); i4 : connectedComponents S o4 = {{0, 1, 2}, {10, 11, 12}, {20, 21, 22}, {30, 31, 32}, {40, 41, 42}} o4 : List

This method was ported from John Stembridge's Maple package available at http://www.math.lsa.umich.edu/~jrs/maple.html#posets.