18.29 Subwords

Module: sage.combinat.subword

Subwords

Module-level Functions

Subwords( w, [k=None])

Returns the combinatorial class of subwords of w.

If k is specified, then it returns the combinatorial class of subwords of w of length k.

sage: S = Subwords(['a','b','c']); S
Subwords of ['a', 'b', 'c']
sage: S.first()
[]
sage: S.last()
['a', 'b', 'c']
sage: S.list()
[[], ['a'], ['b'], ['c'], ['a', 'b'], ['a', 'c'], ['b', 'c'], ['a', 'b',
'c']]

sage: S = Subwords(['a','b','c'], 2); S
Subwords of ['a', 'b', 'c'] of length 2
sage: S.list()
[['a', 'b'], ['a', 'c'], ['b', 'c']]

smallest_positions( word, subword, [pos=0])

Returns the smallest positions for which subword apppears as a subword of word. If pos is specified, then it returns the positions of the first appearance of subword starting at pos.

If subword is not found in word, then it returns False

sage: sage.combinat.subword.smallest_positions([1,2,3,4], [2,4])
[1, 3]
sage: sage.combinat.subword.smallest_positions([1,2,3,4,4], [2,4])
[1, 3]
sage: sage.combinat.subword.smallest_positions([1,2,3,3,4,4], [3,4])
[2, 4]
sage: sage.combinat.subword.smallest_positions([1,2,3,3,4,4], [3,4],2)
[2, 4]
sage: sage.combinat.subword.smallest_positions([1,2,3,3,4,4], [3,4],3)
[3, 4]
sage: sage.combinat.subword.smallest_positions([1,2,3,4], [2,3])
[1, 2]
sage: sage.combinat.subword.smallest_positions([1,2,3,4], [5,5])
False

Class: Subwords_w

class Subwords_w

Subwords_w( self, w)

TESTS:

sage: S = Subwords([1,2,3])
sage: S == loads(dumps(S))
True

Functions: count, $\,$ first, $\,$ iterator, $\,$ last

count( self)

sage: Subwords([1,2,3]).count()
8

first( self)

sage: Subwords([1,2,3]).first()
[]

iterator( self)

sage: [sw for sw in Subwords([1,2,3])]
[[], [1], [2], [3], [1, 2], [1, 3], [2, 3], [1, 2, 3]]

last( self)

sage: Subwords([1,2,3]).last()
[1, 2, 3]

Special Functions: __init__, $\,$ __repr__

__repr__( self)

TESTS:

sage: repr(Subwords([1,2,3]))
'Subwords of [1, 2, 3]'

Class: Subwords_wk

class Subwords_wk

Subwords_wk( self, w, k)

TESTS:

sage: S = Subwords([1,2,3],2)
sage: S == loads(dumps(S))
True

Functions: count, $\,$ first, $\,$ iterator, $\,$ last

count( self)

Returns the number of subwords of w of length k.

sage: Subwords([1,2,3], 2).count()
3

first( self)

sage: Subwords([1,2,3],2).first()
[1, 2]
sage: Subwords([1,2,3],0).first()
[]

iterator( self)

sage: [sw for sw in Subwords([1,2,3],2)]
[[1, 2], [1, 3], [2, 3]]
sage: [sw for sw in Subwords([1,2,3],0)]
[[]]

last( self)

sage: Subwords([1,2,3],2).last()
[2, 3]

Special Functions: __init__, $\,$ __repr__

__repr__( self)

TESTS:

sage: repr(Subwords([1,2,3],2))
'Subwords of [1, 2, 3] of length 2'

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