Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`Combinatorics`
MultisetStrictAscents |
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Examples
(1)
Basic Examples
(1)
PermutationAscents does not work with multisets.
In[1]:=
 | PermutationAscents |
Out[1]=
PermutationAscents[{1,1,2,2,3,3}]
You have to use this function.
In[2]:=
| MultisetStrictAscents |
Out[2]=
{{2},{4}}
In[3]:=
Extract{1,1,2,2,3,3},
[{1,1,2,2,3,3}]
| MultisetStrictAscents |
Out[3]=
{1,2}
In[4]:=
Partition[{1,1,2,2,3,3},2,1]
Out[4]=
{{1,1},{1,2},{2,2},{2,3},{3,3}}
Here are the ascents.
In[5]:=
ExtractPartition[{1,1,2,2,3,3},2,1],
[{1,1,2,2,3,3}]
| MultisetStrictAscents |
Out[5]=
{{1,2},{2,3}}
Make a plot.
In[6]:=
ListPlot[{1,1,2,2,3,3}]
Out[6]=
In[7]:=
ListLinePlot[{1,1,2,2,3,3}]
Out[7]=
This is useful for finding the ascents of a Stirling permutation.
In[8]:=
| StirlingPermutations |
Out[8]=
{{3,3,2,2,1,1},{2,3,3,2,1,1},{2,2,3,3,1,1},{2,2,1,3,3,1},{2,2,1,1,3,3},{3,3,1,2,2,1},{1,3,3,2,2,1},{1,2,3,3,2,1},{1,2,2,3,3,1},{1,2,2,1,3,3},{3,3,1,1,2,2},{1,3,3,1,2,2},{1,1,3,3,2,2},{1,1,2,3,3,2},{1,1,2,2,3,3}}
In[9]:=
FromDigits/@
[3]
| StirlingPermutations |
Out[9]=
{332211,233211,223311,221331,221133,331221,133221,123321,122331,122133,331122,133122,113322,112332,112233}
In[10]:=
SelectLength
[#]1&
[3]
| MultisetStrictAscents |
| StirlingPermutations |
Out[10]=
{{2,3,3,2,1,1},{2,2,3,3,1,1},{2,2,1,3,3,1},{2,2,1,1,3,3},{3,3,1,2,2,1},{1,3,3,2,2,1},{3,3,1,1,2,2},{1,1,3,3,2,2}}
In[11]:=
FromDigits/@SelectLength
[#]1&
[3]
| MultisetStrictAscents |
| StirlingPermutations |
Out[11]=
{233211,223311,221331,221133,331221,133221,331122,113322}
In[12]:=
LengthFromDigits/@SelectLength
[#]1&
[3]
| MultisetStrictAscents |
| StirlingPermutations |
Out[12]=
8
This the EulerianNumberOfTheSecondKind with 3 and 1.
In[13]:=
| EulerianNumberOfTheSecondKind |
Out[13]=
8
We write this as .
8
3 |
1 |
In[14]:=
8;
3 |
1 |
 |
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""