def Klazar_occurrences(pi, pattern):

    """

    Return the number of occurrences of pattern in pi.

​

    EXAMPLES:

​

    From Mansour 2013, page 86, Example 3.24

​

    The set partition π = 135/26/4 contains four occurrences of

    the pattern 12/3, namely, 13/6, 13/4, 15/6, and 35/6. On the other hand, the

    set partition π avoids the pattern 12/34.

​

    sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3]])

    4

    sage: Klazar_occurrences([[1,3,5],[2,6],[4]], [[1,2],[3,4]])

    0

    """

    pi = SetPartition(pi).standardization()

    pattern = SetPartition(pattern).standardization()

    count = 0

    for s in Subsets(range(1,1+pi.size()), pattern.size()):

        if pi.restriction(s).standardization() == pattern:

            count += 1

    return count

​

​

def statistic(pi):

    return Klazar_occurrences(pi, [[1,2,3]])

​

parent_initializer = SetPartitions

element_repr = lambda X: str(sorted([sorted(s) for s in X])).replace("[","{").replace("]","}")

levels = [2, 3, 4, 5]

for level in levels:

    for elt in parent_initializer(level):

        print('%s  =>  %s' % (element_repr(elt), statistic(elt)))