HasseDiagrams

Hasse diagrams are drawings of Posets (partially ordered sets).

Basic Usage

To create a Hasse diagram for a Poset and draw it on the screen, do this:

julia> using Posets, HasseDiagrams

julia> p = subset_lattice(3)
{8, 19} Int64 poset

julia> h = HasseDiagram(p)
Hasse diagram of a {8, 19} Int64 poset

julia> draw(h)

Note that h contains a copy of p, so subsequent changes to p are not reflected in h.

Creating a Layout

When a Hasse diagram is created, it is given a default layout. Hasse diagrams can be given an alternative layout with the function set_xy!. There are two forms:

• set_xy!(h, method) uses the function method to compute the layout. The function acts on the posets held inside h. The list of available layout methods is in the next section.
• set_xy!(h, xy) uses the dictionary xy to site the vertices. Vertex v is placed at xy[v]. If v is not a key of xy, then its location is unchanged.

Scaling

The function scale!(p,μ) multiplies all coordinates in the embedding by μ. It is likely more useful just to multiply the x- or y-coordinates; to do so, use scalex! or scaley!, respecitvely.

Layout Methods

• basic_layout places vertices vertically based on their rank and, within each rank, the horizontal placement is evenly spaced.
• dim2_layout is a decent layout function that is applicable to posets whose dimension is at most two. Reasonbly quick. If the poset has dimension greater than two, a reasonable alternative is presented.
• layered_layout is a Sugiyaqma style layout from the LayeredLayouts module. Can be slow.

Sample Results

Results for a randomly generated two-dimensional poset:

Properties

Font size

• Use set_font_size!(h, sz) to set labels to be sz points. Use 0 to hide labels. Default is FONT_SIZE = 10.
• Use get_font_size(h) to determine the current font size for h.

Node radius

• Use set_radius!(h, r) to set the size of the circles that represent the elements of the poset. Default is RADIUS = 12.
• Use get_radius(h) to determine the current radius.

Fill color

• Use set_fill_color!(h, c) to set the fill color for the circles to c. Default is FILL_COLOR = :white. All circles are filled with the same color.
• Use get_fill_color(h) to determine the current color.

Example

Here is an example for drawing (small) subset lattices with sensible labels. Here is the function to produce the picture:

using Posets, HasseDiagrams, SimpleDrawing, ShowSet

function draw_bool(k)
    p = subset_lattice(k)
    h = HasseDiagram(p)
    labs = Dict{Int,String}()
    for v in 1:nv(p)
        labs[v] = string(subset_decode(v))
    end
    set_labels!(h, labs)
    set_font_size!(h, 8)
    set_radius!(h, 30)
    set_fill_color!(h, :lightblue)
    set_xy!(h, layered_layout)
    draw(h)
    expand_canvas()  # from SimpleDrawing
end

Here is the result of draw_bool(4):