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Combinatorics

Tutorials

  • Combinatorics
  • Combinatorics-1
  • Combinatorics-2

Guides

  • Combinatorics
  • Functions I understand in combinatorics

Tech Notes

  • Combinatorics

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
  • DominatingIntegerPartitionQ
  • DurfeeSquare
  • EnumerateMultisetPartialDerangements
  • EulerianCatalanNumber
  • EulerianNumber
  • EulerianNumberOfTheSecondKind
  • FerrersDiagram
  • Fibbinary
  • FibonacciEncode
  • FindAscentElements
  • FindAscentPositions
  • FrobeniusSymbolFromPartition
  • FromInversionVector
  • FromPartitionPlusNotation
  • FromPartitionSuperscriptNotation
  • GaussFactorial
  • GrayCode
  • HasseDiagram
  • HookLengths
  • HuffmanCodeWords
  • HuffmanDecode
  • HuffmanEncode
  • IntegerPartitionQ
  • InverseFibonacci
  • InverseGrayCode
  • InversionCount
  • InversionVectorQ
  • LehmerCodeFromPermutation
  • LucasNumberU1
  • LucasNumberV2
  • ModifiedCentralBinomialCoefficient
  • Multichoose
  • MultisetAssociation
  • MultisetPartialDerangements
  • MultisetStrictDescentElements
  • MultisetStrictDescents
  • NarayanaNumber
  • NextPermutation
  • NumberOfTableaux
  • OrderedTupleFromIndex
  • OrderedTupleIndex
  • OrderlessCombinations
  • OrderlessCombinationsOfUnmarkedElements
  • PartialOrderGraphQ
  • PartitionCrank
  • PartitionFromFrobeniusSymbol
  • PartitionPlusNotation
  • PartitionRank
  • PartitionSuperscriptNotation
  • PermutationAscents
  • PermutationCountByInversions
  • PermutationDescents
  • PermutationFromIndex
  • PermutationGraph
  • PermutationIndex
  • PermutationMajorIndex
  • PermutationToTableaux
  • Phitorial
  • PosetQ
  • PosetToTableau
  • Primorial
  • QExponential
  • QMultinomial
  • RandomYoungTableau
  • RationalNumberRepeatingDecimalPeriod
  • ReflexiveGraphQ
  • SecantNumber
  • SelectPermutations
  • SelectSubsets
  • SelectTuples
  • SelfConjugatePartitionQ
  • SignedLahNumber
  • StandardYoungTableaux
  • StrictIntegerPartitions
  • SubsetFromIndex
  • SubsetIndex
  • TableauQ
  • TableauToPoset
  • TableauxToPermutation
  • TangentNumber
  • ToInversionVector
  • TransitiveGraphQ
  • TransposeTableau
  • TupleFromIndex
  • TupleIndex
  • UnsignedLahNumber
  • YoungDiagram
  • ZeckendorfRepresentation
PeterBurbery`Combinatorics`
PermutationAscents
​
PermutationAscents
[p]
gives the indices
i
where
p
i
<
p
i+1
, where the permutation
p={
p
1
,
p
2
,…,
p
n
}
is written as a list.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
Consider the permutation:
In[1]:=
p={2,8,1,5,4,7,6,3,9};
Its ascents are at the indices 1, 3, 5, 8, corresponding to
2<8
,
1<5
,
4<7
,
3<9
:
In[2]:=
PermutationAscents
@p
Out[2]=
{1,3,5,8}
The descents follow easily:
In[3]:=
ReverseLength@p-
PermutationAscents
@Reverse@p
Out[3]=
{2,4,6,7}
Possible Issues  
(1)

SeeAlso
Permutations
 
▪
PermutationList
 
▪
PermutationListQ
 
▪
EulerianNumber
RelatedGuides
▪
Combinatorics
RelatedLinks
Permutation Ascent—Wolfram MathWorld
EulerianNumber—Wolfram MathWorld
PermutationAscents
Resource Function contributed by Wolfram Staff
""

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