Generator

latin

A generator in the computation library, called 7 times across 2 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.

latin 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

Two orthogonal Latin squares of order 5Two Latin squares side by side and their superposition, in which every pair of symbols appears exactly once.first0123412340234013401240123second0241313024241303024141302superimposed00122431431123304204223441031033400214214401132032two squares of order 5, each Latin, and their 25 superimposed pairs are all differentthe pairs were collected into a set and counted — one repeat would have made the set smaller

show: "transversal"

Transversals of the cyclic square of order 6A cyclic Latin square with a transversal marked if it has one, beside a count of transversals at neighbouring orders.order 6, symbols 0…5012345123450234501345012450123501234transversals of the cyclic squareorder 33order 40order 515order 60order 7133the cyclic square of order 6 has no transversal at all: all 720 placements were tried and every one repeats asymbola square with no transversal cannot have an orthogonal mate, so the search for one need never begin

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

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