BinaryStrings

The $2^n$ binary strings of length $n$, in standard binary counting order.

✓ checked against that system · ! checked, with disagreements (hover a chip)OEISA000079✓↗A320487✓↗A011782✓↗A131577✓↗A034008✓↗A166444✓↗

BinaryStrings(n)the binary strings of length $n$

CombinatoricaMap[Function[s, Table[Boole[MemberQ[s, i]], {i, n}]], BinarySubsets[Range[n]]]

Typed signatures

Type	Package	Applies
(integer<0..>) -> indexed_collection<list<integer>>	combinatorics	always

Domain: Collections

Definition

Epsil, as the implementation runs it.

count(_n)

1 if _n == 0 else 2 ^ _n

unrank(_n, _r)

Map(
     Function((_r - _r % 2 ^ (_n - j)) / 2 ^ (_n - j) % 2 + 0, j),
     Range(1, _n, 1),
   )

rank(_n, _x)

Fold(Function(acc * 2 + (_x[j] - 0), acc, j), 0, Range(1, _n, 1))

valid(_n, _x)

Length(_x) == _n && Fold(Function(
                                   ok_j && 0 <= _x[j] && _x[j] <= 2 + 0 - 1,
                                   ok_j,
                                   j,
                                 ), True, Range(1, Length(_x), 1))

Examples

Basic #

$2^4$ strings

live ↗

In$\mathrm{Count}(\mathrm{BinaryStrings}(4))$Out$16$

All of length 3, in counting order

live ↗

In$\mathrm{Take}(\mathrm{BinaryStrings}(3), 8)$Out$\bigl\lbrack\bigl\lbrack0, 0, 0\bigr\rbrack, \bigl\lbrack0, 0, 1\bigr\rbrack, \bigl\lbrack0, 1, 0\bigr\rbrack, \bigl\lbrack0, 1, 1\bigr\rbrack, \bigl\lbrack1, 0, 0\bigr\rbrack, \bigl\lbrack1, 0, 1\bigr\rbrack, \bigl\lbrack1, 1, 0\bigr\rbrack, \bigl\lbrack1, 1, 1\bigr\rbrack\bigr\rbrack$

About

Examples	2
Checked against	Combinatorica 2 agree
Crosswalk	OEIS ×6Combinatorica

Implementation

mappedcombinatoricapackages/oracle/src/mappings.ts

Combinatorica lists binary counting as subsets; the word of a subset has a 1 at each element.

See also: BinaryWords