Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Determine if one integer partition dominates another
Since 5+1<4+3, the first partition does not dominate the second:
In[1]:= | ![]() |
Out[1]= | ![]() |
The first partition dominates the second, since 4≥4, 4+4≥4+3 and 4+4≥4+3+1:
In[2]:= | ![]() |
Out[2]= | ![]() |
Display the domination lattice on integer partitions, using the resource function HasseDiagram:
In[3]:= | ![]() |
In[4]:= | ![]() |
Out[4]= | ![]() |
DominatingIntegerPartitionQ[p,q] being False does not imply that DominatingIntegerPartitionQ[q,p] is True:
In[5]:= | ![]() |
In[6]:= | ![]() |
Out[6]= | ![]() |
In[7]:= | ![]() |
Out[7]= | ![]() |
In this case, this is because the first element of q is smaller than the first element of p:
In[8]:= | ![]() |
Out[8]= | ![]() |
DominatingIntegerPartitionQ[p,q] and DominatingIntegerPartitionQ[q,p] can both yield True for certain p and q:
In[9]:= | ![]() |
Out[9]= | ![]() |
In[10]:= | ![]() |
Out[10]= | ![]() |
In[11]:= | ![]() |
Out[11]= | ![]() |
Among the partitions of n, {n} is always the largest and {1,…,1} is the smallest:
In[12]:= | ![]() |
Out[13]= | ![]() |
This work is licensed under a Creative Commons Attribution 4.0 International License