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Combinatorics

Tutorials

  • Combinatorics

Guides

  • Combinatorics
  • Functions I understand in combinatorics

Tech Notes

  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
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  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
  • Fibbinary
  • FibonacciEncode
  • FindAscentElements
  • FindAscentPositions
  • FindDescentElements
  • FindDescentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
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  • IntegerPartitionQ
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  • InversionCount
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PeterBurbery`Combinatorics`
FindAscentPositions
​
FindAscentPositions
[multi]
finds the positions of ascents in the multiset
multi
.
​
Details and Options

Examples  
(3)
Basic Examples  
(1)
Consider this random permutation.
In[1]:=
randomPermutation=RandomSample[Range[9]]
Out[1]=
{6,7,1,8,5,3,2,9,4}
Find the positions, that is the indices, of the ascents. An index i is an ascent index if
a
i
<
a
i+1
.
In[2]:=
FindAscentPositions
[randomPermutation]
Out[2]=
{{1},{3},{7}}
Find the ascents.
In[3]:=
FindAscentElements
[randomPermutation]
Out[3]=
{{6,7},{1,8},{2,9}}
Write this with Inactive.
In[4]:=
Inactive[Less]@@@
FindAscentElements
[randomPermutation]
Out[4]=
{6<7,1<8,2<9}
Are all these statements true?
In[5]:=
AllTrue[Activate[#]&]Inactive[Less]@@@
FindAscentElements
[randomPermutation]
Out[5]=
True
Reverse with greater:
In[6]:=
Inactive[Greater]@@@Map[Reverse]
FindAscentElements
[randomPermutation]
Out[6]=
{7>6,8>1,9>2}
Are all these statements true?
In[7]:=
AllTrue[Activate[#]&]Inactive[Greater]@@@Map[Reverse]
FindAscentElements
[randomPermutation]
Out[7]=
True
Scope  
(1)

Options  
(1)

SeeAlso
FindAscentElements
RelatedGuides
▪
Combinatorics
""

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