Generator

ferrers

A generator in the number library, called 7 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

ferrers is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

The partition 5 + 4 + 2 + 1 and its conjugateA row of dots for each part, and the same dots read down the columns instead.5 + 4 + 2 + 14 + 3 + 2 + 2 + 1read downboth are partitions of 12: the same dots, counted along the rows and then down the columnsand turning the diagram over a second time gives back what it started as

show: "glaisher"

Partitions of 8: odd parts against distinct partsTwo lists of partitions, one restricted to odd parts and one to distinct parts, drawn as rows of dots.into odd parts7+15+35+1+1+13+3+1+13+1+1+1+1+11+1+1+1+1+1+1+1into distinct parts87+16+25+35+2+14+3+16 of each, for 8 — and the same is true of every number anyone has triednothing in either list suggests why, which is what makes the bijection worth having

show: "durfee"

The Durfee square of 6 + 5 + 5 + 3 + 2 + 1The largest square of dots that fits in the corner of a Ferrers diagram, with the arm and the leg it leaves.3 × 3the square holds 9 dots, the arm to its right 7, the leg below it 6and 9 + 7 + 6 = 22, which is every dot exactly once

What it checks while it draws

Collected by running the family and listening to lib/verify.js, not written here. The count is how many separate times this build put that claim to the test.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

The whole library · What the figures prove