def max_sackin(n):
"""
Returns all the `Shape` instances that attain the maximum Sackin index with `int` n leaves.
:param n: `int` instance.
:return: `list` instance.
"""
return [comb(n)]
def min_quartet(n):
"""
Returns all the `Shape` instances that attain the minimum Quartet index with `int` n leaves.
:param n: `int` instance.
:return: `list` instance.
"""
return [comb(n)]
def maxcolless(n):
"""
Returns all the `Shape` instances that attain the maximum Colless index with `int` n leaves.
:param n: `int` instance.
:return: `list` instance.
"""
return [comb(n)]
def max_var_depths(n):
"""
Returns all the `Shape` instances that attain the maximum variance of depths with `int` n leaves.
:param n: `int` instance.
:return: `list` instance.
"""
return (n - 1) * (n - 2) * (n**2 + 3 * n - 6) / (12 * n**2), comb(n)
def max_cophenetic(n):
"""
Returns all the `Shape` instances that attain the maximum Cophenetic index with `int` n leaves.
:param n: `int` instance.
:return: `list` instance.
"""
return [comb(n)]
def min_automorphisms(n):
"""
Returns all the `Shape` instances that attain the minimum number of automorphisms with `int` n leaves.
:param n: `int` instance.
:return: `list` instance.
"""
return [comb(n)]