SmallestPartsFunction | Example Notebook

Here is an illustrative example. Start with the integer partitions of 3:

In[76]:=

IntegerPartitions@3

Out[76]=

{{3},{2,1},{1,1,1}}

Here are their smallest parts:

In[77]:=

Min/@IntegerPartitions@3

Out[77]=

{3,1,1}

Compute the number of smallest parts per partition:

In[78]:=

Count[#,Min[#]]&/@IntegerPartitions@3

Out[78]=

{1,1,3}

Find their total:

In[67]:=

Total@%

Out[67]=

5

This is precisely the value returned by

SmallestPartsFunction

:

[◼]	SmallestPartsFunction

[3]

Out[62]=

5

———

Here are the first 10 numbers in the smallest part function (denoted

spt

) sequence (OEIS A092269):

[◼]	SmallestPartsFunction

/@Range@10

Out[68]=

{1,3,5,10,14,26,35,57,80,119}