Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
PeterBurbery`Combinatorics`
EulerianNumber |
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Details and Options
Examples
(7)
Basic Examples
(3)
The table of Eulerian numbers up to 10:
In[1]:=
GridTable
[n,k],{n,10},{k,n},FrameAll
 | EulerianNumber |
Out[1]=
1 | | | | | | | | | |
1 | 1 | | | | | | | | |
1 | 4 | 1 | | | | | | | |
1 | 11 | 11 | 1 | | | | | | |
1 | 26 | 66 | 26 | 1 | | | | | |
1 | 57 | 302 | 302 | 57 | 1 | | | | |
1 | 120 | 1191 | 2416 | 1191 | 120 | 1 | | | |
1 | 247 | 4293 | 15619 | 15619 | 4293 | 247 | 1 | | |
1 | 502 | 14608 | 88234 | 156190 | 88234 | 14608 | 502 | 1 | |
1 | 1013 | 47840 | 455192 | 1310354 | 1310354 | 455192 | 47840 | 1013 | 1 |
Consider the permutation:
In[1]:=
p={2,8,1,5,4,7,6,3,9};
Here are its four ascents, corresponding to , , , :
2<8
1<5
4<7
3<9
In[2]:=
 | PermutationAscents |
Out[2]=
{1,3,5,8}
This counts the number of ascents of the 24 permutations of :
{1,2,3,4}
In[1]:=
Length@*
/@Permutations@Range[4]
 | PermutationAscents |
Out[1]=
{3,2,2,2,2,1,2,1,2,2,2,1,2,1,1,1,2,1,2,1,1,1,1,0}
This tallies up permutations by the number of ascents:
In[2]:=
Last/@Tally[Sort@Flatten@%]
Out[2]=
{1,11,11,1}
This gives the same list, calculated without implicitly listing the individual ascents:
In[3]:=
| EulerianNumber |
Out[3]=
{1,11,11,1}
Scope
(2)
Properties & Relations
(1)
Neat Examples
(1)
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