@enumeratio/cli

Enumerate a combinatorial collection from the terminal and stream its elements to stdout — a thin driver over enumeratio-client (the pure-SQL core in PGlite), and the home of the sage oracle tests.

enumeratio permutations size=4                  # one element per line, canonical order
enumeratio arrangements size=5 length=2         # a chain grade fixes a secondary axis
enumeratio permutations size=8 | head           # streams with backpressure — pipe-friendly
enumeratio integer_partitions size=20 --count   # just |collection(...)|  ->  627

Prefer to poke at it without installing? The Playground runs this same grammar against an in-browser database, with clickable examples.

An argument is name=value: size=N is the primary dimension, any other key names a grade in the collection's chain (arrangements' length, words' base, subsets' k). Output streams in rank windows, so pipes just work with no limit; enumeration runs PGlite in-process (Ctrl-C, or wrap with the shell timeout, to cap a runaway).

Discovering what's there

enumeratio list                 # the realized collections
enumeratio list set_partitions  # one collection's catalog shape (axes, stats, reprs)
enumeratio table                # every collection at once, as an aligned grid

Distributions and triangles

-g <stat> gives a statistic's distribution (count per value, plus a total/mode/mean summary); --triangle <stat> splits that distribution per fiber, so a size range prints the classic combinatorial triangle:

enumeratio permutations size=4 -g inversions          # the Mahonian distribution + summary
enumeratio permutations size=1:6 --triangle inversions # the Mahonian triangle over sizes 1..6
enumeratio set_partitions size=1:5 --triangle blocks   # Stirling of the second kind

Maps and composition

maps shows the map graph — every map as a source → codomain edge — and -m/--through apply maps to the elements you enumerate. --through composes a chain across collections (each map's codomain feeds the next):

enumeratio maps                                        # the whole map graph
enumeratio maps permutations                           # just the edges out of permutations
enumeratio permutations size=3 -m to_lehmer_code,descent_set  # each map's image as a column
enumeratio permutations size=3 --through rsk_insertion,shape  # permutation → RSK tableau → its shape

--at ADDR inspects a single element — a rank, or an @serialization — as a card of its rank, every statistic, and every map image:

enumeratio permutations size=4 --at @2413   # 2413's inversions, cycle type, RSK tableau, Lehmer code, …

Other options: --range lo:hi slices the canonical order, --repr <name> picks an alternate rendering, --count / --stats / --json / --fields A,B shape the output. The explorer is the same client behind a UI.