notatio

The collection explorer ​

Every collection head (Derangements, SymmetricGroup, Subsets, …) gets a table on its symbol page, drawn by <notatio-collection-table> and derived from the head's record. A hand-written enumerate: in the record wins field by field; whatever it leaves out is derived.

What is derived ​

  • The call: the head at a small size, from its grades and maxSize. A head with no maxSize stops at size 6.
  • A glyph for the carrier's elements, from the carrier record's glyph:.
  • Columns: statistics defined on the carrier that answer on the first row, most-used first. A statistic that is constant over the default collection is left out.

A head that is catalog-only, untyped, or not opening as a collection gets no table.

Pickers ​

The table has a statistics menu (add or remove columns, with a text filter for a carrier with hundreds of statistics) and a size stepper bounded as the derivation is. An explicit expr with no size or template stays fixed.

In a notebook the same choices are options:

  • Columns -> Automatic: the derived columns. The element needs its statistics property set, since the runtime loads no records.
  • Glyph -> Automatic: the carrier's glyph.
  • Size -> n: the size of the collection.

Distributions ​

Each statistic column has a distribution button. It opens a pane drawing how often each value occurs over the whole collection, as a bar chart with its generating polynomial. Distribution -> True opens it from the start.

Descents and inversions over the permutations of five

source · editable

The tally is computed in the browser on demand, by the page's kernel or engine; nothing is precomputed. A collection past size-max, with too many elements to walk, or of unknown size declines with the reason instead of freezing. A column that is an expression rather than a statistic head has no distribution.

On a statistic's page ​

A statistic's own page shows its distribution over its carrier's collection as a triangle: the coefficients row by row, the generating polynomial and a bar chart of the last row. The "same distribution as" button scans the other statistics on the carrier for equidistribution, row by row, within a time budget, and lists the matches. The collection is derived from the carrier's records as the table's is.

Try it ​

The same size bounds govern the Try it panel: where no example of a collection head lifts to a control, Try it falls back to the explorer's sized call.