Words

The strings of length $size$ over a $base$-letter alphabet $\{1, …, base\}$.

SageMathsage.combinat.words.words.Words(base, size)↗SymPyvariations↗mathlib4List.Vector

Words(size, base)the strings of length $size$ over a $base$-letter alphabet $\{1, …, base\}$

Typed signatures

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

Domain: Collections

Details

• Count is $base^{size}$; the same family as Tuples, with grades reordered.

Definition

Epsil, as the implementation runs it.

count(_size, _base)

1 if _size == 0 else _base ^ _size

unrank(_size, _base, _r)

Map(Function(
              (_r - _r % _base ^ (_size - j)) / _base ^ (_size - j) % _base + 1,
              j,
            ), Range(1, _size, 1))

rank(_size, _base, _x)

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

valid(_size, _base, _x)

Length(_x) == _size && Fold(
                             Function(ok_j && 1 <= _x[j] && _x[j] <= _base + 1 -
                                                                     1, ok_j, j),
                             True,
                             Range(1, Length(_x), 1),
                           )

Enumeration

Examples

1 more kept as data, checked against the oracles

Basic #

$Count(Words(3, 2)) = 8$

live ↗

In$\mathrm{Count}(\mathrm{Words}(3, 2))$Out$8$

The first element in enumeration order

live ↗

In$\mathrm{Words}(3, 2)[1]$Out${\operatorname{Word}}([1, 1, 1])$

About

Examples	3
Crosswalk	SageMathSymPymathlib4

See also: Tuples, BinaryWords