Pictorial representations of combinatorial elements, rendered by <notatio-figure>. Each is requested explicitly by kind + a MathJSON integer value (the shape a collection head yields at a given index). Colours theme from --notatio-accent / --notatio-border / --notatio-fg.
One filled dot per row i at column image[i] — the one-line word 3 1 2. A pictorial glyph (à la MatrixPlot); the true bracketed matrix is MatrixForm, a TeX representation still to come.
<notatio-figure kind="permutation" value="[3,1,2]" />n sets how many cells to draw; members are filled. Without it, n defaults to the largest member.
<notatio-figure kind="subset" value="[1,3]" n="6" /> The Ferrers shape of the partition, its cells numbered 1…n in reading order — the superstandard filling, always a valid standard Young tableau (rows increase rightward, columns downward).
<notatio-figure kind="tableau" value="[3,2,1]" />
<notatio-figure kind="tableau" value="[4,2]" />
<notatio-figure kind="tableau" value="[2,2,2]" />value[i] is the block of element i+1 (a restricted-growth string). Each block draws as a pill of its elements — [0,0,1,0,2] is {1,2,4} {3} {5}.
<notatio-figure kind="set-partition" value="[0,0,1,0,2]" /> A monotone staircase of unit steps east (0) and north (1) across the grid it spans; counts C(a+b, a).
<notatio-figure kind="lattice" value="[0,1,1,0,1,0]" />
<notatio-figure kind="lattice" value="[1,0,1,0,0,1]" />1 is an internal node (always two children), 0 a leaf, listed in preorder. Tidy layout: leaves take sequential x, each internal node sits over the mean of its children. The five shapes of size 3 (Catalan again):
<notatio-figure kind="binary-tree" value="[1,1,0,0,1,0,0]" />
<notatio-figure kind="binary-tree" value="[1,1,1,0,0,0,0]" />
<notatio-figure kind="binary-tree" value="[1,1,0,1,0,0,0]" />
<notatio-figure kind="binary-tree" value="[1,0,1,1,0,0,0]" />
<notatio-figure kind="binary-tree" value="[1,0,1,0,1,0,0]" />tree reads each entry as that node's number of children, so any rooted ordered tree draws: here a root with three children, the middle one a cherry, the last a chain.
<notatio-figure kind="tree" value="[3,0,2,0,0,1,0]" />The generic escape hatch: hand it a ready-made SVG string and it renders it verbatim (for representations authored elsewhere).
<notatio-figure svg='<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 40 40" role="img" aria-label="star"><polygon points="20,2 25,15 39,15 28,24 32,38 20,30 8,38 12,24 1,15 15,15" fill="var(--notatio-accent,#d97706)"/></svg>' />