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Combinatorics

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  • Functions I understand in combinatorics

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  • Combinatorics
  • Stirling permutation

Symbols

  • CanonicalMultiset
  • CentralBinomialCoefficient
  • ConjugatePartition
  • DescendingSublists
  • DivisorHasseDiagram
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  • FindAscentElements
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  • FindDescentElements
  • FindDescentPositions
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PeterBurbery`Combinatorics`
FindDescentElements
​
FindDescentElements
[multi]
returns the sets of adjacent elements in the multiset multi where the second element of the set of adjacent elements is less than the first element of the set of adjacent elements.
​
Details and Options

Examples  
(3)
Basic Examples  
(1)
Consider this random permutation.
In[1]:=
randomPermutation=RandomSample[Range[9]]
Out[1]=
{9,1,3,4,7,5,8,6,2}
Find the positions, that is the indices, of the descent. An index i is an descent index if
a
i
>
a
i+1
.
In[2]:=
FindDescentElements
[randomPermutation]
Out[2]=
{{9,1},{7,5},{8,6},{6,2}}
Find the descents.
In[3]:=
FindDescentElements
[randomPermutation]
Out[3]=
{{9,1},{7,5},{8,6},{6,2}}
Write this with Inactive.
In[4]:=
Inactive[Greater]@@@
FindDescentElements
[randomPermutation]
Out[4]=
{9>1,7>5,8>6,6>2}
Are all these statements true?
In[5]:=
AllTrue[Activate[#]&]Inactive[Greater]@@@
FindDescentElements
[randomPermutation]
Out[5]=
True
Reverse with less:
In[6]:=
Inactive[Less]@@@Map[Reverse]
FindDescentElements
[randomPermutation]
Out[6]=
{1<9,5<7,6<8,2<6}
Are all these statements true?
In[7]:=
AllTrue[Activate[#]&]Inactive[Less]@@@Map[Reverse]
FindDescentElements
[randomPermutation]
Out[7]=
True
Scope  
(1)

Options  
(1)

SeeAlso
FindAscentElements
 
▪
FindDescentPositions
 
▪
FindAscentPositions
RelatedGuides
▪
Combinatorics
""

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